# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int x^5ln\left(x\right)\:dx$

Learn how to solve trigonometric integrals problems step by step online.

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

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(x^5*ln(x))dx. Use the integration by parts theorem to calculate the integral \int x^5\ln\left(x\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

$\frac{1}{6}\left(x^5\left(x\ln\left(x\right)-x\right)+\frac{5}{6}x^{6}\right)+C_0$

### Problem Analysis

$\int x^5ln\left(x\right)\:dx$

### Main topic:

Trigonometric integrals

~ 0.13 seconds