# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\sin\left(2x\right) e^xdx$

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(sin(2*x)*2.718281828459045^x)dx. Use the integration by parts theorem to calculate the integral \int e^x\sin\left(2x\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

$\frac{2}{5}e^x\sin\left(x\right)\cos\left(x\right)-\frac{2}{5}e^x\cos\left(2x\right)+C_0$

### Problem Analysis

$\int\sin\left(2x\right) e^xdx$

### Main topic:

Trigonometric integrals

~ 0.18 seconds