Question

Evaluate $\int \frac{x^7}{x-1}dx$

Answer 1

$\int \frac{x^{7}dx}{x-1}$

$=\int (x^6+x^5+x^4+x^3+x^2+x+1)dx+\int \frac{dx}{x-1}$

$=\frac{x^7}{7}+\frac{x^6}{6}+\frac{x^5}{5}+\frac{x^4}{4}+\frac{x^3}{3}+\frac{x^2}{2}+x+\log |x-1|+c$