Sr Examen
Integral de 1/(3+2x^2+5x^4) dx
Solución
Ha introducido
[src]
oo / | | 1 | --------------- dx | 2 4 | 3 + 2*x + 5*x | / 1
$$\int\limits_{1}^{\infty} \frac{1}{5 x^{4} + \left(2 x^{2} + 3\right)}\, dx$$
Integral(1/(3 + 2*x^2 + 5*x^4), (x, 1, oo))
Respuesta (Indefinida)
[src]
_______________________________________ _______________________________________ / _______________ / / ____________ ____________ ____________ ____________\ ____________ ____________\ _______________ / / ____________ ____________ ____________ ____________\ ____________ ____________\ / ____________ / ____________ ____________ ____________ ____________ \ / ____________ / ____________ ____________ ____________ ____________ \ | / ____ | ____ | ____ / ____ ____ / ____ ____ / ____ / ____ | ___ / ____ ____ / ____ | / ____ | ____ | ____ / ____ ____ / ____ ____ / ____ / ____ | ___ / ____ ____ / ____ | / ____ ___ / ____ | / ____ ____ / ____ ____ ___ / ____ / ____ | / ____ ___ / ____ | / ____ ____ / ____ ____ ___ / ____ / ____ | | 1 / 1 \/ 15 | 103 2 244*\/ 15 | 4*\/ 35 *\/ 1 + \/ 15 4*\/ 21 *\/ 1 + \/ 15 \/ 42 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | 57*\/ 2 *\/ 8 + \/ 15 32*\/ 30 *\/ 8 + \/ 15 | / 1 \/ 15 | 103 2 244*\/ 15 | 4*\/ 21 *\/ 1 + \/ 15 4*\/ 35 *\/ 1 + \/ 15 \/ 42 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | 57*\/ 2 *\/ 8 + \/ 15 32*\/ 30 *\/ 8 + \/ 15 | / 1 \/ 15 \/ 2 *\/ 8 + \/ 15 | 12*\/ 1 + \/ 15 4*\/ 15 *\/ 1 + \/ 15 10*x*\/ 21 3*\/ 2 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | / 1 \/ 15 \/ 2 *\/ 8 + \/ 15 | 12*\/ 1 + \/ 15 4*\/ 15 *\/ 1 + \/ 15 10*x*\/ 21 3*\/ 2 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | | --------------- dx = C + / ---- + ------ *log|- --- + x + ---------- + x*|- ------------------------ + ------------------------ + --------------------------------------| - ------------------------ + -------------------------| - / ---- + ------ *log|- --- + x + ---------- + x*|- ------------------------ + ------------------------ - --------------------------------------| - ------------------------ + -------------------------| + 2* / ---- + ------ - --------------------- *atan|- -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------| + 2* / ---- + ------ - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| | 2 4 \/ 1344 1344 \ 175 525 \ 35 35 35 / 175 525 / \/ 1344 1344 \ 175 525 \ 35 35 35 / 175 525 / \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| | 3 + 2*x + 5*x | / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ | | / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ | | | / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ | | / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ | / \ 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 / \14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 /
$$\int \frac{1}{5 x^{4} + \left(2 x^{2} + 3\right)}\, dx = C + \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(x^{2} + x \left(- \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35}\right) - \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{103}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{244 \sqrt{15}}{525} \right)} - \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(x^{2} + x \left(- \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} - \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35}\right) - \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{103}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{244 \sqrt{15}}{525} \right)} + 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(\frac{10 \sqrt{21} x}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} + 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(\frac{10 \sqrt{21} x}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)}$$
Gráfica
Respuesta
[src]
_______________________________________ _______________________________________ ________________________________________
_______________ / ____________ ____________ ____________ ____________ ____________ ____________\ _______________ / ____________ ____________ ____________ ____________ ____________ ____________\ / ____________ / ____________ ____________ ____________ ____________ \ / ____________ / ____________ ____________ ____________ ____________ \ / ____________
/ ____ | ____ ___ / ____ ____ / ____ ____ / ____ ____ / ____ ____ / ____ / ____ | / ____ | ____ ___ / ____ ____ / ____ ____ / ____ ____ / ____ ____ / ____ / ____ | / ____ ___ / ____ | / ____ ____ ____ / ____ ___ / ____ / ____ | / ____ ___ / ____ | ____ / ____ ____ / ____ ___ / ____ / ____ | ____ / ____ ___ / ____
/ 1 \/ 15 | 72 244*\/ 15 57*\/ 2 *\/ 8 + \/ 15 4*\/ 21 *\/ 1 + \/ 15 4*\/ 35 *\/ 1 + \/ 15 32*\/ 30 *\/ 8 + \/ 15 \/ 42 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | / 1 \/ 15 | 72 244*\/ 15 57*\/ 2 *\/ 8 + \/ 15 4*\/ 35 *\/ 1 + \/ 15 4*\/ 21 *\/ 1 + \/ 15 32*\/ 30 *\/ 8 + \/ 15 \/ 42 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | / 1 \/ 15 \/ 2 *\/ 8 + \/ 15 | 12*\/ 1 + \/ 15 10*\/ 21 4*\/ 15 *\/ 1 + \/ 15 3*\/ 2 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | / 1 \/ 15 \/ 2 *\/ 8 + \/ 15 | 10*\/ 21 12*\/ 1 + \/ 15 4*\/ 15 *\/ 1 + \/ 15 3*\/ 2 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | pi*\/ 21 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15
/ ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- - --------------------------------------| - / ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- + --------------------------------------| - 2* / ---- + ------ - --------------------- *atan|- -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------| - 2* / ---- + ------ - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------
\/ 1344 1344 \175 525 175 35 35 525 35 / \/ 1344 1344 \175 525 175 35 35 525 35 / \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| 84
| / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ | | / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ |
| / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ | | / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ |
\ 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 / \14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 /
$$- 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(- \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{10 \sqrt{21}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} - \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(- \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{72}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} + \frac{244 \sqrt{15}}{525} \right)} - 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(- \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{10 \sqrt{21}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} + \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(- \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} - \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{72}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{244 \sqrt{15}}{525} \right)} + \frac{\sqrt{21} \pi \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}}{84}$$
=
=
_______________________________________ _______________________________________ ________________________________________
_______________ / ____________ ____________ ____________ ____________ ____________ ____________\ _______________ / ____________ ____________ ____________ ____________ ____________ ____________\ / ____________ / ____________ ____________ ____________ ____________ \ / ____________ / ____________ ____________ ____________ ____________ \ / ____________
/ ____ | ____ ___ / ____ ____ / ____ ____ / ____ ____ / ____ ____ / ____ / ____ | / ____ | ____ ___ / ____ ____ / ____ ____ / ____ ____ / ____ ____ / ____ / ____ | / ____ ___ / ____ | / ____ ____ ____ / ____ ___ / ____ / ____ | / ____ ___ / ____ | ____ / ____ ____ / ____ ___ / ____ / ____ | ____ / ____ ___ / ____
/ 1 \/ 15 | 72 244*\/ 15 57*\/ 2 *\/ 8 + \/ 15 4*\/ 21 *\/ 1 + \/ 15 4*\/ 35 *\/ 1 + \/ 15 32*\/ 30 *\/ 8 + \/ 15 \/ 42 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | / 1 \/ 15 | 72 244*\/ 15 57*\/ 2 *\/ 8 + \/ 15 4*\/ 35 *\/ 1 + \/ 15 4*\/ 21 *\/ 1 + \/ 15 32*\/ 30 *\/ 8 + \/ 15 \/ 42 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | / 1 \/ 15 \/ 2 *\/ 8 + \/ 15 | 12*\/ 1 + \/ 15 10*\/ 21 4*\/ 15 *\/ 1 + \/ 15 3*\/ 2 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | / 1 \/ 15 \/ 2 *\/ 8 + \/ 15 | 10*\/ 21 12*\/ 1 + \/ 15 4*\/ 15 *\/ 1 + \/ 15 3*\/ 2 *\/ 1 + \/ 15 *\/ 8 + \/ 15 | pi*\/ 21 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15
/ ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- - --------------------------------------| - / ---- + ------ *log|--- + ---------- - ------------------------ - ------------------------ + ------------------------ + ------------------------- + --------------------------------------| - 2* / ---- + ------ - --------------------- *atan|- -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------| - 2* / ---- + ------ - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------
\/ 1344 1344 \175 525 175 35 35 525 35 / \/ 1344 1344 \175 525 175 35 35 525 35 / \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| 84
| / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ | | / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ |
| / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ | | / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ |
\ 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 / \14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 14*\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 + \/ 2 *\/ 8 + \/ 15 *\/ 1 + 3*\/ 15 - 2*\/ 2 *\/ 8 + \/ 15 /
$$- 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(- \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{10 \sqrt{21}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} - \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(- \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{72}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} + \frac{244 \sqrt{15}}{525} \right)} - 2 \sqrt{- \frac{\sqrt{2} \sqrt{\sqrt{15} + 8}}{672} + \frac{1}{1344} + \frac{\sqrt{15}}{448}} \operatorname{atan}{\left(- \frac{3 \sqrt{2} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} - \frac{12 \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{4 \sqrt{15} \sqrt{1 + \sqrt{15}}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} + \frac{10 \sqrt{21}}{\sqrt{2} \sqrt{\sqrt{15} + 8} \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}} + 14 \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}} \right)} + \sqrt{\frac{1}{1344} + \frac{\sqrt{15}}{1344}} \log{\left(- \frac{57 \sqrt{2} \sqrt{\sqrt{15} + 8}}{175} - \frac{\sqrt{42} \sqrt{1 + \sqrt{15}} \sqrt{\sqrt{15} + 8}}{35} - \frac{4 \sqrt{21} \sqrt{1 + \sqrt{15}}}{35} + \frac{72}{175} + \frac{32 \sqrt{30} \sqrt{\sqrt{15} + 8}}{525} + \frac{4 \sqrt{35} \sqrt{1 + \sqrt{15}}}{35} + \frac{244 \sqrt{15}}{525} \right)} + \frac{\sqrt{21} \pi \sqrt{- 2 \sqrt{2} \sqrt{\sqrt{15} + 8} + 1 + 3 \sqrt{15}}}{84}$$
sqrt(1/1344 + sqrt(15)/1344)*log(72/175 + 244*sqrt(15)/525 - 57*sqrt(2)*sqrt(8 + sqrt(15))/175 - 4*sqrt(21)*sqrt(1 + sqrt(15))/35 + 4*sqrt(35)*sqrt(1 + sqrt(15))/35 + 32*sqrt(30)*sqrt(8 + sqrt(15))/525 - sqrt(42)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/35) - sqrt(1/1344 + sqrt(15)/1344)*log(72/175 + 244*sqrt(15)/525 - 57*sqrt(2)*sqrt(8 + sqrt(15))/175 - 4*sqrt(35)*sqrt(1 + sqrt(15))/35 + 4*sqrt(21)*sqrt(1 + sqrt(15))/35 + 32*sqrt(30)*sqrt(8 + sqrt(15))/525 + sqrt(42)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/35) - 2*sqrt(1/1344 + sqrt(15)/448 - sqrt(2)*sqrt(8 + sqrt(15))/672)*atan(-12*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 10*sqrt(21)/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 4*sqrt(15)*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) - 3*sqrt(2)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))))) - 2*sqrt(1/1344 + sqrt(15)/448 - sqrt(2)*sqrt(8 + sqrt(15))/672)*atan(10*sqrt(21)/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 12*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) - 4*sqrt(15)*sqrt(1 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))) + 3*sqrt(2)*sqrt(1 + sqrt(15))*sqrt(8 + sqrt(15))/(14*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))) + sqrt(2)*sqrt(8 + sqrt(15))*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15))))) + pi*sqrt(21)*sqrt(1 + 3*sqrt(15) - 2*sqrt(2)*sqrt(8 + sqrt(15)))/84
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.