Integral of ln(x^3)x^2
Answer
$\frac{1}{3}\left(3x^3\ln\left(x\right)-x^3\right)+C_0$
Step-by-step explanation
Problem to solve:
$\int\ln\left(x^3\right)x^2dx$
1
Solve the integral $\int x^2\ln\left(x^3\right)dx$ applying u-substitution. Let $u$ and $du$ be
$\begin{matrix}u=x^3 \\ du=3x^{2}dx\end{matrix}$
2
Isolate $dx$ in the previous equation
$\frac{du}{3x^{2}}=dx$
Answer
$\frac{1}{3}\left(3x^3\ln\left(x\right)-x^3\right)+C_0$