Step-by-step Solution

Integrate $x^2\ln\left(x\right)$ with respect to x

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Step-by-step explanation

Problem to solve:

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

Learn how to solve calculus problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Unlock this full step-by-step solution!

Learn how to solve calculus problems step by step online. Calculate the integral of x^2ln(x). We can solve the integral \int x^2\ln\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

Final Answer

$\frac{x^{3}\ln\left(x\right)}{3}-\frac{1}{9}x^{3}+C_0$
$\int x^2\ln\left(x\right)dx$

Main topic:

Calculus

Related formulas:

3. See formulas

Time to solve it:

~ 0.09 s (SnapXam)