Sr Examen
Integral de dx/(1+x^3) dx
Solución
Ha introducido
[src]
oo / | | 1 | ------ dx | 3 | 1 + x | / 1
$$\int\limits_{1}^{\infty} \frac{1}{x^{3} + 1}\, dx$$
Integral(1/(1 + x^3), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ |2*\/ 3 *(-1/2 + x)| | / 2 \ \/ 3 *atan|------------------| | 1 log\1 + x - x/ log(1 + x) \ 3 / | ------ dx = C - --------------- + ---------- + ------------------------------ | 3 6 3 3 | 1 + x | /
$$\int \frac{1}{x^{3} + 1}\, dx = C + \frac{\log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{1}{2}\right)}{3} \right)}}{3}$$
Gráfica
Respuesta
[src]
/ -2*pi*I / pi*I\ 2*pi*I / 5*pi*I\\
| ------- | ----| ------ | ------||
| / pi*I\ 3 | 3 | 3 | 3 ||
| 2*log\1 - e / 2*e *log\1 - e / 2*e *log\1 - e /|
|- ---------------- - ------------------------- - --------------------------|*Gamma(2/3)
\ 3 3 3 /
----------------------------------------------------------------------------------------
3*Gamma(5/3)
$$\frac{\left(- \frac{2 e^{\frac{2 i \pi}{3}} \log{\left(1 - e^{\frac{5 i \pi}{3}} \right)}}{3} - \frac{2 \log{\left(1 - e^{i \pi} \right)}}{3} - \frac{2 e^{- \frac{2 i \pi}{3}} \log{\left(1 - e^{\frac{i \pi}{3}} \right)}}{3}\right) \Gamma\left(\frac{2}{3}\right)}{3 \Gamma\left(\frac{5}{3}\right)}$$
=
=
/ -2*pi*I / pi*I\ 2*pi*I / 5*pi*I\\
| ------- | ----| ------ | ------||
| / pi*I\ 3 | 3 | 3 | 3 ||
| 2*log\1 - e / 2*e *log\1 - e / 2*e *log\1 - e /|
|- ---------------- - ------------------------- - --------------------------|*Gamma(2/3)
\ 3 3 3 /
----------------------------------------------------------------------------------------
3*Gamma(5/3)
$$\frac{\left(- \frac{2 e^{\frac{2 i \pi}{3}} \log{\left(1 - e^{\frac{5 i \pi}{3}} \right)}}{3} - \frac{2 \log{\left(1 - e^{i \pi} \right)}}{3} - \frac{2 e^{- \frac{2 i \pi}{3}} \log{\left(1 - e^{\frac{i \pi}{3}} \right)}}{3}\right) \Gamma\left(\frac{2}{3}\right)}{3 \Gamma\left(\frac{5}{3}\right)}$$
(-2*log(1 - exp_polar(pi*i))/3 - 2*exp(-2*pi*i/3)*log(1 - exp_polar(pi*i/3))/3 - 2*exp(2*pi*i/3)*log(1 - exp_polar(5*pi*i/3))/3)*gamma(2/3)/(3*gamma(5/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.