Sr Examen
Integral de arctgsqrt(2x-1) dx
Solución
Ha introducido
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1 / | | _________ | atan(x)*\/ 2*x - 1 dx | / 0
$$\int\limits_{0}^{1} \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}\, dx$$
Integral(atan(x)*sqrt(2*x - 1), (x, 0, 1))
Respuesta (Indefinida)
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/ / 3\\ / | 4 2 | __________ 28*t 256*t || | __________ 4*RootSum|4096*t + 1408*t + 125, t -> t*log|\/ -1 + 2*x + ---- + ------|| 3/2 | _________ 4*\/ -1 + 2*x \ \ 5 5 // (-1 + 2*x) *atan(x) | atan(x)*\/ 2*x - 1 dx = C - -------------- - ---------------------------------------------------------------------------- + --------------------- | 3 3 3 /
$$\int \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}\, dx = C + \frac{\left(2 x - 1\right)^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{3} - \frac{4 \sqrt{2 x - 1}}{3} - \frac{4 \operatorname{RootSum} {\left(4096 t^{4} + 1408 t^{2} + 125, \left( t \mapsto t \log{\left(\frac{256 t^{3}}{5} + \frac{28 t}{5} + \sqrt{2 x - 1} \right)} \right)\right)}}{3}$$
Gráfica
Respuesta
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______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________
/ ___________ / ___________ ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ ___________ \
/ ___ ___ / ___ | ___ / ___ ____ / ___ ___ / ___ / ___ | / ___ ___ / ___ | ___ / ___ / ___ / ___ ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | ___ ___ / ___ ____ / ___ / ___ / ___ | / ___ ___ / ___ | ___ ___ / ___ / ___ / ___ ____ / ___ |
/ 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 2*I*\/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | \/ 2 *\/ 1 + \/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 2*I*\/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 3*\/ 1 + \/ 5 2*I \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 3*\/ 1 + \/ 5 2*I \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 3*\/ 1 + \/ 5 2 \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 2 3*\/ 1 + \/ 5 \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 2*\/ 5 \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 2*\/ 5 \/ 2 *\/ 1 + \/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 |
40* / --- + ------- - -------------------- *atan|-------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------| 40* / --- + ------- - -------------------- *atan|- -------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------| _____________ / / ___________ ___________ ___________\ ___________ ___________\ _____________ / ___________ ___________ ___________ ___________ ___________\ 16* / --- + ------- - -------------------- *atan|- ------------------------------------------ + --------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------| 16* / --- + ------- - -------------------- *atan|------------------------------------------ + --------------------------------------------------------- - --------------------------------------------------------- - ---------------------------------------------------------| _____________ _____________ _____________ _____________ 16* / --- + ------- - -------------------- *atan|- ------------------------------------------ + --------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------| 16* / --- + ------- - -------------------- *atan|--------------------------------------------------------- + ------------------------------------------ - --------------------------------------------------------- - ---------------------------------------------------------| _____________ / / ___________ ___________ ___________\ ___________ ___________\ _____________ / ___________ ___________ ___________ ___________ ___________\ 40* / --- + ------- - -------------------- *atan|-------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------| 40* / --- + ------- - -------------------- *atan|-------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------|
\/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________| / ___ | ___ | ___________ ____ / ___ ___ / ___ / ___ | ___ / ___ ____ / ___ | / ___ | ___ ___________ ___ / ___ ____ / ___ ____ / ___ ___ / ___ / ___ | \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| / ___ / / ___________ ___________ ___________ ___________\ ___________ ___________\ / ___ / ___________ ___________ ___________ ___________ ___________ ___________\ / ___ / / ___________ ___________ ___________ ___________\ ___________ ___________\ / ___ / ___________ ___________ ___________ ___________ ___________ ___________\ \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| / ___ | ___ | ___________ ____ / ___ ___ / ___ / ___ | ___ / ___ ____ / ___ | / ___ | ___ ___________ ___ / ___ ____ / ___ ____ / ___ ___ / ___ / ___ | \/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________|
| ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ | | ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ | / 1 \/ 5 |8 22*\/ 5 | ___ / ___ \/ 10 *\/ 1 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 3 + \/ 5 | / 1 \/ 5 |18 22*\/ 5 ___ / ___ 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 1 + \/ 5 \/ 10 *\/ 3 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | | / ___________ ___________ / ___________ ___________ / ___________ ___________ / ___________ | | / ___________ ___________ / ___________ ___________ / ___________ ___________ / ___________ | / 1 \/ 5 | ___ | ___ / ___ ____ / ___ / ___ / ___ | ___ / ___ ____ / ___ | / 1 \/ 5 | ___ ___ / ___ ___ / ___ ____ / ___ / ___ / ___ ____ / ___ | / 1 \/ 5 | ___ | ___ / ___ / ___ / ___ ____ / ___ | ___ / ___ ____ / ___ | / 1 \/ 5 | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ / ___ / ___ | | / ___________ ___________ / ___________ ___________ / ___________ ___________ / ___________ | | ___________ / ___________ / ___________ ___________ / ___________ ___________ / ___________ | / 1 \/ 5 |8 22*\/ 5 | ___ / ___ \/ 10 *\/ 1 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 3 + \/ 5 | / 1 \/ 5 |18 22*\/ 5 ___ / ___ 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 1 + \/ 5 \/ 10 *\/ 3 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | | ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ | | ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ |
| / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ | | / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ | 20* / --- + ----- *log|- + -------- + I*|- 2*\/ 2 *\/ 1 + \/ 5 + --------------------- + -------------------------------------| - ----------------------- + ---------------------| 20* / --- + ----- *log|-- + -------- + 2*\/ 2 *\/ 1 + \/ 5 - ----------------------- - --------------------- + --------------------- - -------------------------------------| | / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | | / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | 8* / --- + ----- *log\42 + 24*\/ 5 + I*\- \/ 2 *\/ 1 + \/ 5 - 2*\/ 10 *\/ 1 + \/ 5 + 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 / - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 / 8* / --- + ----- *log\44 + 24*\/ 5 + \/ 2 *\/ 1 + \/ 5 - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 - 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 + 2*\/ 10 *\/ 1 + \/ 5 / 8* / --- + ----- *log\42 + 24*\/ 5 + I*\\/ 2 *\/ 1 + \/ 5 - 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 + 2*\/ 10 *\/ 1 + \/ 5 / - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 / 8* / --- + ----- *log\44 + 24*\/ 5 - \/ 2 *\/ 1 + \/ 5 - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 - 2*\/ 10 *\/ 1 + \/ 5 + 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 / | / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | | / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | 20* / --- + ----- *log|- + -------- + I*|2*\/ 2 *\/ 1 + \/ 5 - --------------------- - -------------------------------------| - ----------------------- + ---------------------| 20* / --- + ----- *log|-- + -------- - 2*\/ 2 *\/ 1 + \/ 5 - ----------------------- + --------------------- + --------------------- + -------------------------------------| | / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ | | / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ |
4 pi 4*I \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \ \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \/ 640 640 \5 5 \ 5 5 / 5 5 / \/ 640 640 \5 5 5 5 5 5 / \ \/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \/ 128 128 \/ 128 128 \/ 128 128 \/ 128 128 \ \/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \/ 640 640 \5 5 \ 5 5 / 5 5 / \/ 640 640 \5 5 5 5 5 5 / \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 /
- - + -- + --- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
$$- \frac{4}{3} - \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} - 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3} + \sqrt{2} \sqrt{1 + \sqrt{5}} + 2 \sqrt{10} \sqrt{1 + \sqrt{5}} + 44 + 24 \sqrt{5} \right)}}{3} - \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} - \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5} - \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{18}{5} + 2 \sqrt{2} \sqrt{1 + \sqrt{5}} + \frac{22 \sqrt{5}}{5} \right)}}{3} + \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} - 2 \sqrt{10} \sqrt{1 + \sqrt{5}} - \sqrt{2} \sqrt{1 + \sqrt{5}} + 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3} + 44 + 24 \sqrt{5} \right)}}{3} + \frac{\pi}{12} + \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} - 2 \sqrt{2} \sqrt{1 + \sqrt{5}} + \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{18}{5} + \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5} + \frac{22 \sqrt{5}}{5} \right)}}{3} - \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{8}{5} + \frac{22 \sqrt{5}}{5} + i \left(- 2 \sqrt{2} \sqrt{1 + \sqrt{5}} + \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5}\right) \right)}}{3} + \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{8}{5} + \frac{22 \sqrt{5}}{5} + i \left(- \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5} - \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + 2 \sqrt{2} \sqrt{1 + \sqrt{5}}\right) \right)}}{3} - \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5} i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5} i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} + 42 + 24 \sqrt{5} + i \left(- 2 \sqrt{10} \sqrt{1 + \sqrt{5}} - \sqrt{2} \sqrt{1 + \sqrt{5}} + 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}\right) \right)}}{3} + \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} + 42 + 24 \sqrt{5} + i \left(- 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3} + \sqrt{2} \sqrt{1 + \sqrt{5}} + 2 \sqrt{10} \sqrt{1 + \sqrt{5}}\right) \right)}}{3} + \frac{4 i}{3}$$
=
=
______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________
/ ___________ / ___________ ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ ___________ \ / ___________ / ___________ ___________ ___________ ___________ \
/ ___ ___ / ___ | ___ / ___ ____ / ___ ___ / ___ / ___ | / ___ ___ / ___ | ___ / ___ / ___ / ___ ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | / ___ ___ / ___ ____ / ___ | / ___ ___ / ___ | ___ ___ / ___ ____ / ___ / ___ / ___ | / ___ ___ / ___ | ___ ___ / ___ / ___ / ___ ____ / ___ |
/ 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 2*I*\/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | \/ 2 *\/ 1 + \/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 2*I*\/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 3*\/ 1 + \/ 5 2*I \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 3*\/ 1 + \/ 5 2*I \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 3*\/ 1 + \/ 5 2 \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 2 3*\/ 1 + \/ 5 \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 2*\/ 5 \/ 2 *\/ 1 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 | / 1 3*\/ 5 \/ 2 *\/ 3 + \/ 5 | 2*\/ 5 \/ 2 *\/ 1 + \/ 5 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 2*\/ 10 *\/ 1 + \/ 5 |
40* / --- + ------- - -------------------- *atan|-------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------| 40* / --- + ------- - -------------------- *atan|- -------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------| _____________ / / ___________ ___________ ___________\ ___________ ___________\ _____________ / ___________ ___________ ___________ ___________ ___________\ 16* / --- + ------- - -------------------- *atan|- ------------------------------------------ + --------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------| 16* / --- + ------- - -------------------- *atan|------------------------------------------ + --------------------------------------------------------- - --------------------------------------------------------- - ---------------------------------------------------------| _____________ _____________ _____________ _____________ 16* / --- + ------- - -------------------- *atan|- ------------------------------------------ + --------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------| 16* / --- + ------- - -------------------- *atan|--------------------------------------------------------- + ------------------------------------------ - --------------------------------------------------------- - ---------------------------------------------------------| _____________ / / ___________ ___________ ___________\ ___________ ___________\ _____________ / ___________ ___________ ___________ ___________ ___________\ 40* / --- + ------- - -------------------- *atan|-------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------| 40* / --- + ------- - -------------------- *atan|-------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------|
\/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________| / ___ | ___ | ___________ ____ / ___ ___ / ___ / ___ | ___ / ___ ____ / ___ | / ___ | ___ ___________ ___ / ___ ____ / ___ ____ / ___ ___ / ___ / ___ | \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| / ___ / / ___________ ___________ ___________ ___________\ ___________ ___________\ / ___ / ___________ ___________ ___________ ___________ ___________ ___________\ / ___ / / ___________ ___________ ___________ ___________\ ___________ ___________\ / ___ / ___________ ___________ ___________ ___________ ___________ ___________\ \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 128 128 64 | ______________________________________ ______________________________________ ______________________________________ ______________________________________| / ___ | ___ | ___________ ____ / ___ ___ / ___ / ___ | ___ / ___ ____ / ___ | / ___ | ___ ___________ ___ / ___ ____ / ___ ____ / ___ ___ / ___ / ___ | \/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________| \/ 640 640 320 | ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________|
| ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ | | ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ | / 1 \/ 5 |8 22*\/ 5 | ___ / ___ \/ 10 *\/ 1 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 3 + \/ 5 | / 1 \/ 5 |18 22*\/ 5 ___ / ___ 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 1 + \/ 5 \/ 10 *\/ 3 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | | / ___________ ___________ / ___________ ___________ / ___________ ___________ / ___________ | | / ___________ ___________ / ___________ ___________ / ___________ ___________ / ___________ | / 1 \/ 5 | ___ | ___ / ___ ____ / ___ / ___ / ___ | ___ / ___ ____ / ___ | / 1 \/ 5 | ___ ___ / ___ ___ / ___ ____ / ___ / ___ / ___ ____ / ___ | / 1 \/ 5 | ___ | ___ / ___ / ___ / ___ ____ / ___ | ___ / ___ ____ / ___ | / 1 \/ 5 | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ / ___ / ___ | | / ___________ ___________ / ___________ ___________ / ___________ ___________ / ___________ | | ___________ / ___________ / ___________ ___________ / ___________ ___________ / ___________ | / 1 \/ 5 |8 22*\/ 5 | ___ / ___ \/ 10 *\/ 1 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 3 + \/ 5 | / 1 \/ 5 |18 22*\/ 5 ___ / ___ 18*\/ 2 *\/ 3 + \/ 5 \/ 10 *\/ 1 + \/ 5 \/ 10 *\/ 3 + \/ 5 3*\/ 5 *\/ 1 + \/ 5 *\/ 3 + \/ 5 | | ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ | | ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ ___________ / ___________ / ___________ |
| / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ | | / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ | 20* / --- + ----- *log|- + -------- + I*|- 2*\/ 2 *\/ 1 + \/ 5 + --------------------- + -------------------------------------| - ----------------------- + ---------------------| 20* / --- + ----- *log|-- + -------- + 2*\/ 2 *\/ 1 + \/ 5 - ----------------------- - --------------------- + --------------------- - -------------------------------------| | / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | | / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | 8* / --- + ----- *log\42 + 24*\/ 5 + I*\- \/ 2 *\/ 1 + \/ 5 - 2*\/ 10 *\/ 1 + \/ 5 + 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 / - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 / 8* / --- + ----- *log\44 + 24*\/ 5 + \/ 2 *\/ 1 + \/ 5 - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 - 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 + 2*\/ 10 *\/ 1 + \/ 5 / 8* / --- + ----- *log\42 + 24*\/ 5 + I*\\/ 2 *\/ 1 + \/ 5 - 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 + 2*\/ 10 *\/ 1 + \/ 5 / - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 / 8* / --- + ----- *log\44 + 24*\/ 5 - \/ 2 *\/ 1 + \/ 5 - 18*\/ 2 *\/ 3 + \/ 5 - 5*\/ 10 *\/ 3 + \/ 5 - 2*\/ 10 *\/ 1 + \/ 5 + 3*\/ 1 + \/ 5 *\/ 3 + \/ 5 / | / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | | / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ / ___ / ___ ___ / ___ | 20* / --- + ----- *log|- + -------- + I*|2*\/ 2 *\/ 1 + \/ 5 - --------------------- - -------------------------------------| - ----------------------- + ---------------------| 20* / --- + ----- *log|-- + -------- - 2*\/ 2 *\/ 1 + \/ 5 - ----------------------- + --------------------- + --------------------- + -------------------------------------| | / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ | | / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ / ___ / ___ ___ / ___ ___ / ___ ___ / ___ |
4 pi 4*I \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \ \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \/ 640 640 \5 5 \ 5 5 / 5 5 / \/ 640 640 \5 5 5 5 5 5 / \ \/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \/ 128 128 \/ 128 128 \/ 128 128 \/ 128 128 \ \/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \/ 640 640 \5 5 \ 5 5 / 5 5 / \/ 640 640 \5 5 5 5 5 5 / \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 / \\/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 \/ 3 + \/ 5 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 + 2*\/ 2 *\/ 1 + 3*\/ 5 - 2*\/ 2 *\/ 3 + \/ 5 /
- - + -- + --- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
$$- \frac{4}{3} - \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} - 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3} + \sqrt{2} \sqrt{1 + \sqrt{5}} + 2 \sqrt{10} \sqrt{1 + \sqrt{5}} + 44 + 24 \sqrt{5} \right)}}{3} - \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} - \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5} - \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{18}{5} + 2 \sqrt{2} \sqrt{1 + \sqrt{5}} + \frac{22 \sqrt{5}}{5} \right)}}{3} + \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} - 2 \sqrt{10} \sqrt{1 + \sqrt{5}} - \sqrt{2} \sqrt{1 + \sqrt{5}} + 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3} + 44 + 24 \sqrt{5} \right)}}{3} + \frac{\pi}{12} + \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} + \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} - 2 \sqrt{2} \sqrt{1 + \sqrt{5}} + \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{18}{5} + \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5} + \frac{22 \sqrt{5}}{5} \right)}}{3} - \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{8}{5} + \frac{22 \sqrt{5}}{5} + i \left(- 2 \sqrt{2} \sqrt{1 + \sqrt{5}} + \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5}\right) \right)}}{3} + \frac{20 \sqrt{\frac{1}{640} + \frac{\sqrt{5}}{640}} \log{\left(- \frac{18 \sqrt{2} \sqrt{\sqrt{5} + 3}}{5} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 3}}{5} + \frac{8}{5} + \frac{22 \sqrt{5}}{5} + i \left(- \frac{3 \sqrt{5} \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{5} - \frac{\sqrt{10} \sqrt{1 + \sqrt{5}}}{5} + 2 \sqrt{2} \sqrt{1 + \sqrt{5}}\right) \right)}}{3} - \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5} i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{40 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{320} + \frac{1}{640} + \frac{3 \sqrt{5}}{640}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{5} i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}} + 2 \sqrt{2} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{16 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{5} + 3}}{64} + \frac{1}{128} + \frac{3 \sqrt{5}}{128}} \operatorname{atan}{\left(- \frac{2 \sqrt{10} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} - \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{3 \sqrt{1 + \sqrt{5}}}{\sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} + \frac{2 i}{\sqrt{\sqrt{5} + 3} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{5} + 3} + 1 + 3 \sqrt{5}}} \right)}}{3} - \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} + 42 + 24 \sqrt{5} + i \left(- 2 \sqrt{10} \sqrt{1 + \sqrt{5}} - \sqrt{2} \sqrt{1 + \sqrt{5}} + 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3}\right) \right)}}{3} + \frac{8 \sqrt{\frac{1}{128} + \frac{\sqrt{5}}{128}} \log{\left(- 18 \sqrt{2} \sqrt{\sqrt{5} + 3} - 5 \sqrt{10} \sqrt{\sqrt{5} + 3} + 42 + 24 \sqrt{5} + i \left(- 3 \sqrt{1 + \sqrt{5}} \sqrt{\sqrt{5} + 3} + \sqrt{2} \sqrt{1 + \sqrt{5}} + 2 \sqrt{10} \sqrt{1 + \sqrt{5}}\right) \right)}}{3} + \frac{4 i}{3}$$
-4/3 + pi/12 + 4*i/3 - 40*sqrt(1/640 + 3*sqrt(5)/640 - sqrt(2)*sqrt(3 + sqrt(5))/320)*atan(sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 2*i*sqrt(5)/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3 - 40*sqrt(1/640 + 3*sqrt(5)/640 - sqrt(2)*sqrt(3 + sqrt(5))/320)*atan(-sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 2*i*sqrt(5)/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3 - 20*sqrt(1/640 + sqrt(5)/640)*log(8/5 + 22*sqrt(5)/5 + i*(-2*sqrt(2)*sqrt(1 + sqrt(5)) + sqrt(10)*sqrt(1 + sqrt(5))/5 + 3*sqrt(5)*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/5) - 18*sqrt(2)*sqrt(3 + sqrt(5))/5 + sqrt(10)*sqrt(3 + sqrt(5))/5)/3 - 20*sqrt(1/640 + sqrt(5)/640)*log(18/5 + 22*sqrt(5)/5 + 2*sqrt(2)*sqrt(1 + sqrt(5)) - 18*sqrt(2)*sqrt(3 + sqrt(5))/5 - sqrt(10)*sqrt(1 + sqrt(5))/5 + sqrt(10)*sqrt(3 + sqrt(5))/5 - 3*sqrt(5)*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/5)/3 - 16*sqrt(1/128 + 3*sqrt(5)/128 - sqrt(2)*sqrt(3 + sqrt(5))/64)*atan(-3*sqrt(1 + sqrt(5))/sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*i/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3 - 16*sqrt(1/128 + 3*sqrt(5)/128 - sqrt(2)*sqrt(3 + sqrt(5))/64)*atan(3*sqrt(1 + sqrt(5))/sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*i/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3 - 8*sqrt(1/128 + sqrt(5)/128)*log(42 + 24*sqrt(5) + i*(-sqrt(2)*sqrt(1 + sqrt(5)) - 2*sqrt(10)*sqrt(1 + sqrt(5)) + 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))) - 18*sqrt(2)*sqrt(3 + sqrt(5)) - 5*sqrt(10)*sqrt(3 + sqrt(5)))/3 - 8*sqrt(1/128 + sqrt(5)/128)*log(44 + 24*sqrt(5) + sqrt(2)*sqrt(1 + sqrt(5)) - 18*sqrt(2)*sqrt(3 + sqrt(5)) - 5*sqrt(10)*sqrt(3 + sqrt(5)) - 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5)) + 2*sqrt(10)*sqrt(1 + sqrt(5)))/3 + 8*sqrt(1/128 + sqrt(5)/128)*log(42 + 24*sqrt(5) + i*(sqrt(2)*sqrt(1 + sqrt(5)) - 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5)) + 2*sqrt(10)*sqrt(1 + sqrt(5))) - 18*sqrt(2)*sqrt(3 + sqrt(5)) - 5*sqrt(10)*sqrt(3 + sqrt(5)))/3 + 8*sqrt(1/128 + sqrt(5)/128)*log(44 + 24*sqrt(5) - sqrt(2)*sqrt(1 + sqrt(5)) - 18*sqrt(2)*sqrt(3 + sqrt(5)) - 5*sqrt(10)*sqrt(3 + sqrt(5)) - 2*sqrt(10)*sqrt(1 + sqrt(5)) + 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5)))/3 + 16*sqrt(1/128 + 3*sqrt(5)/128 - sqrt(2)*sqrt(3 + sqrt(5))/64)*atan(-3*sqrt(1 + sqrt(5))/sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3 + 16*sqrt(1/128 + 3*sqrt(5)/128 - sqrt(2)*sqrt(3 + sqrt(5))/64)*atan(2/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 3*sqrt(1 + sqrt(5))/sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) - sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3 + 20*sqrt(1/640 + sqrt(5)/640)*log(8/5 + 22*sqrt(5)/5 + i*(2*sqrt(2)*sqrt(1 + sqrt(5)) - sqrt(10)*sqrt(1 + sqrt(5))/5 - 3*sqrt(5)*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/5) - 18*sqrt(2)*sqrt(3 + sqrt(5))/5 + sqrt(10)*sqrt(3 + sqrt(5))/5)/3 + 20*sqrt(1/640 + sqrt(5)/640)*log(18/5 + 22*sqrt(5)/5 - 2*sqrt(2)*sqrt(1 + sqrt(5)) - 18*sqrt(2)*sqrt(3 + sqrt(5))/5 + sqrt(10)*sqrt(1 + sqrt(5))/5 + sqrt(10)*sqrt(3 + sqrt(5))/5 + 3*sqrt(5)*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/5)/3 + 40*sqrt(1/640 + 3*sqrt(5)/640 - sqrt(2)*sqrt(3 + sqrt(5))/320)*atan(2*sqrt(5)/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3 + 40*sqrt(1/640 + 3*sqrt(5)/640 - sqrt(2)*sqrt(3 + sqrt(5))/320)*atan(2*sqrt(5)/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - sqrt(2)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) - 3*sqrt(1 + sqrt(5))*sqrt(3 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))) + 2*sqrt(10)*sqrt(1 + sqrt(5))/(sqrt(3 + sqrt(5))*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5))) + 2*sqrt(2)*sqrt(1 + 3*sqrt(5) - 2*sqrt(2)*sqrt(3 + sqrt(5)))))/3
Respuesta numérica
[src]
(0.22302002743378 + 0.06452467814082j)
(0.22302002743378 + 0.06452467814082j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.