Sr Examen
Integral de 1/(5*x^4+2*x^2+3) dx
Solución
Ha introducido
[src]
oo / | | 1 | --------------- dx | 4 2 | 5*x + 2*x + 3 | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\left(5 x^{4} + 2 x^{2}\right) + 3}\, dx$$
Integral(1/(5*x^4 + 2*x^2 + 3), (x, 1, oo))
Respuesta (Indefinida)
[src]
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------------------------ + -------------------------| - / ---- + ------ *log|- --- + x + ---------- + x*|- ------------------------ + ------------------------ - --------------------------------------| - ------------------------ + -------------------------| + 2* / ---- + ------ - --------------------- *atan|- -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------| + 2* / ---- + ------ - --------------------- *atan|-------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| | 4 2 \/ 1344 1344 \ 175 525 \ 35 35 35 / 175 525 / \/ 1344 1344 \ 175 525 \ 35 35 35 / 175 525 / \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| \/ 1344 448 672 | ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________| | 5*x + 2*x + 3 | / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ | | / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ / ____________ ____________ / ____________ | | | / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ | | / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ / ____ ___ / ____ ___ / ____ / ____ ___ / ____ | / \ 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}{\left(5 x^{4} + 2 x^{2}\right) + 3}\, 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
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.