# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int t e^{\left(5t+\pi \right)}dt$

Learn how to solve integrals of exponential functions problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Learn how to solve integrals of exponential functions problems step by step online. Compute the integral int(t*2.718281828459045^(5*t+3.141592653589793))dt. Use the integration by parts theorem to calculate the integral \int te^{\left(5t+\pi \right)}dt, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

$\frac{1}{5}e^{\left(5t+\pi \right)}t-\frac{1}{25}e^{\left(5t+\pi \right)}+C_0$

### Problem Analysis

$\int t e^{\left(5t+\pi \right)}dt$

### Main topic:

Integrals of Exponential Functions

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