Question 523313
Just use a simple substitution and that is all. By letting u = x^5 + 1 and, du/dx = 5x^4, du = 5x^4 dx,


*[tex \LARGE \int \frac{5x^4}{x^5+1}\,dx = \int \frac{du}{u}]


This is equal to


*[tex \LARGE \ln |u| + C = \ln (x^5 + 1) + C] where C is a constant.