Sr Examen
Integral de x^5/(x^3+1)/(x^2+8) dx
Solución
Ha introducido
[src]
1 / | | / 5 \ | | x | | |------| | | 3 | | \x + 1/ | -------- dx | 2 | x + 8 | / 0
$$\int\limits_{0}^{1} \frac{x^{5} \frac{1}{x^{3} + 1}}{x^{2} + 8}\, dx$$
Integral((x^5/(x^3 + 1))/(x^2 + 8), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | / 5 \ | | x | / ___\ / ___ \ | |------| ___ |x*\/ 2 | ___ |2*\/ 3 *(-1/2 + x)| | | 3 | / 2 \ / 2\ 1024*\/ 2 *atan|-------| \/ 3 *atan|------------------| | \x + 1/ 5*log\1 + x - x/ log(1 + x) 32*log\8 + x / \ 4 / \ 3 / | -------- dx = C + x - ----------------- - ---------- + -------------- - ------------------------ - ------------------------------ | 2 114 27 513 513 171 | x + 8 | /
$$\int \frac{x^{5} \frac{1}{x^{3} + 1}}{x^{2} + 8}\, dx = C + x - \frac{\log{\left(x + 1 \right)}}{27} + \frac{32 \log{\left(x^{2} + 8 \right)}}{513} - \frac{5 \log{\left(x^{2} - x + 1 \right)}}{114} - \frac{1024 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{4} \right)}}{513} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{1}{2}\right)}{3} \right)}}{171}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 2 |
1024*\/ 2 *atan|-----| ___
32*log(8) log(2) 32*log(9) \ 4 / pi*\/ 3
1 - --------- - ------ + --------- - ---------------------- - --------
513 27 513 513 513
$$- \frac{1024 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}}{513} - \frac{32 \log{\left(8 \right)}}{513} - \frac{\log{\left(2 \right)}}{27} - \frac{\sqrt{3} \pi}{513} + \frac{32 \log{\left(9 \right)}}{513} + 1$$
=
=
/ ___\
___ |\/ 2 |
1024*\/ 2 *atan|-----| ___
32*log(8) log(2) 32*log(9) \ 4 / pi*\/ 3
1 - --------- - ------ + --------- - ---------------------- - --------
513 27 513 513 513
$$- \frac{1024 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}}{513} - \frac{32 \log{\left(8 \right)}}{513} - \frac{\log{\left(2 \right)}}{27} - \frac{\sqrt{3} \pi}{513} + \frac{32 \log{\left(9 \right)}}{513} + 1$$
1 - 32*log(8)/513 - log(2)/27 + 32*log(9)/513 - 1024*sqrt(2)*atan(sqrt(2)/4)/513 - pi*sqrt(3)/513
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.