Step-by-step Solution

Solve the integral of logarithmic functions $\int x^2\ln\left(x\right)dx$

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Step-by-step Solution

Problem to solve:

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

Solving method

Learn how to solve integrals involving logarithmic functions 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 integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(x^2*ln(x))dx. 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

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