Question

qual a integral de x^8*ln xdx

Answer 1

Vamos por partes:

$\int x^8\ln x\ dx\\\\\\u=\ln x\to du=\dfrac{dx}{x}\\\\dv=x^8\ dx\to v=\dfrac{x^9}{9}\\\\\\\int x^8\ln x\ dx=\\\\\dfrac{x^9\ln x}{9}-\int\dfrac{x^8}{9}\ dx=\\\\\boxed{\dfrac{x^9\ln x}{9}-\dfrac{x^9}{81}+C}$