# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int e^{\left(-1\right)\cdot x}\sin\left(x\right)dx$

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(2.718281828459045^(-1*x)*sin(x))dx. Use the integration by parts theorem to calculate the integral \int e^{-x}\sin\left(x\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

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

### Problem Analysis

$\int e^{\left(-1\right)\cdot x}\sin\left(x\right)dx$

### Main topic:

Trigonometric integrals

~ 0.2 seconds