Question

integration of dx/x+x^5

Answer 1

[math]\int \dfrac{1}{x(x^7+1)} \,dx[/math]
[math]\int \dfrac{x^6}{x^7(x^7+1)} \,dx[/math]
[math]x^7=u[/math]
[math]7x^6\,dx=du[/math]
[math]\dfrac{1}{7}\int \dfrac{1}{u(u+1)} \,du[/math]
[math]\dfrac{1}{7}\int \dfrac{1+u-u}{u(u+1)} \,du[/math]
[math]\dfrac{1}{7}\int \dfrac{1}{u}-\dfrac{1}{u+1} \,du[/math]
[math]\dfrac{1}{7}(\ln u-\ln(u+1))[/math]
[math]\ln\sqrt[7]{\dfrac{u}{u+1}}[/math]
[math]\ln\sqrt[7]{\dfrac{x^7}{x^7+1}}[/math]
[math]\ln\dfrac{x}{\sqrt[7]{x^7+1}}+C[/math]

Answer 2

Hope this is ur required answer.
Proud to help you.