# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\:x\:\sin\left(2x+3\right)dx$

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*sin(2*x+3))dx. Use the integration by parts theorem to calculate the integral \int x\sin\left(2x+3\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

$-\frac{1}{2}x\cos\left(2x+3\right)+\frac{1}{4}\sin\left(2x+3\right)+C_0$

### Problem Analysis

$\int\:x\:\sin\left(2x+3\right)dx$

### Main topic:

Trigonometric integrals

~ 1.44 seconds