# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\left(e^t\cos\left(t\right)\right)dt$

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

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

### Problem Analysis

$\int\left(e^t\cos\left(t\right)\right)dt$

### Main topic:

Trigonometric integrals

~ 0.33 seconds