## Final Answer

## Step-by-step Solution

Problem to solve:

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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

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

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