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\int\ln\left(x^3\right)x^2dx

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

$\frac{du}{3x^{2}}=dx$

Unlock this step-by-step solution!

Answer

$\frac{1}{3}\left(3x^3\ln\left(x\right)-x^3\right)+C_0$
$\int\ln\left(x^3\right)x^2dx$

Main topic:

Integration by substitution

Time to solve it:

~ 1.98 seconds