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

Integrate te^(5t+pi)

Answer

$-\frac{24}{191}e^{\left(\pi +5t\right)}-\frac{1}{25}e^{\left(\pi +5t\right)}+\frac{1}{25}e^{\left(\pi +5t\right)}\left(\pi +5t\right)+C_0$

Step-by-step explanation

Problem

$\int t e^{\left(5t+\pi \right)}dt$
1

Solve the integral $\int e^{\left(\pi +5t\right)}tdt$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=e^{\left(\pi +5t\right)} \\ du=5e^{\left(\pi +5t\right)}dt\end{matrix}$

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Answer

$-\frac{24}{191}e^{\left(\pi +5t\right)}-\frac{1}{25}e^{\left(\pi +5t\right)}+\frac{1}{25}e^{\left(\pi +5t\right)}\left(\pi +5t\right)+C_0$

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