Sr Examen
Integral de (x^n)/(1+x) dx
Solución
Ha introducido
[src]
1 / | | n | x | ----- dx | 1 + x | / 0
$$\int\limits_{0}^{1} \frac{x^{n}}{x + 1}\, dx$$
Integral(x^n/(1 + x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | n n / pi*I \ n / pi*I \ | x x*x *Gamma(1 + n)*lerchphi\x*e , 1, 1 + n/ n*x*x *Gamma(1 + n)*lerchphi\x*e , 1, 1 + n/ | ----- dx = C + --------------------------------------------- + ----------------------------------------------- | 1 + x Gamma(2 + n) Gamma(2 + n) | /
$$\int \frac{x^{n}}{x + 1}\, dx = C + \frac{n x x^{n} \Phi\left(x e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + \frac{x x^{n} \Phi\left(x e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)}$$
Respuesta
[src]
/ pi*I \ / pi*I \
Gamma(1 + n)*lerchphi\e , 1, 1 + n/ n*Gamma(1 + n)*lerchphi\e , 1, 1 + n/
-------------------------------------- + ----------------------------------------
Gamma(2 + n) Gamma(2 + n)
$$\frac{n \Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + \frac{\Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)}$$
=
=
/ pi*I \ / pi*I \
Gamma(1 + n)*lerchphi\e , 1, 1 + n/ n*Gamma(1 + n)*lerchphi\e , 1, 1 + n/
-------------------------------------- + ----------------------------------------
Gamma(2 + n) Gamma(2 + n)
$$\frac{n \Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + \frac{\Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)}$$
gamma(1 + n)*lerchphi(exp_polar(pi*i), 1, 1 + n)/gamma(2 + n) + n*gamma(1 + n)*lerchphi(exp_polar(pi*i), 1, 1 + n)/gamma(2 + n)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.