# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\:x^3sen\:\left(x\right)dx$

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^3*sin(x))dx. Use the integration by parts theorem to calculate the integral \int x^3\sin\left(x\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

$-x^3\cos\left(x\right)+3x^{2}\sin\left(x\right)+6x\cos\left(x\right)-6\sin\left(x\right)+C_0$

### Problem Analysis

$\int\:x^3sen\:\left(x\right)dx$

### Main topic:

Trigonometric integrals

~ 0.25 seconds