What is the integral of x*e^{5x+2} ?

The integral of x*e^{5x+2} is 1/5 e^{5x+2}x-1/25 e^{5x+2}+C

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integral of x*e^{5x+2}

\int x \cdot e^{5 x + 2} d x

\frac{1}{5} e^{5 x + 2} x - \frac{1}{25} e^{5 x + 2} + C

Solution steps

\int x e^{5 x + 2} d x

Apply Integration By Parts

: \frac{1}{5} e^{5 x + 2} x - \int \frac{1}{5} e^{5 x + 2} d x

= \frac{1}{5} e^{5 x + 2} x - \int \frac{1}{5} e^{5 x + 2} d x

\int \frac{1}{5} e^{5 x + 2} d x = \frac{1}{25} e^{5 x + 2}

= \frac{1}{5} e^{5 x + 2} x - \frac{1}{25} e^{5 x + 2}

Add a constant to the solution

= \frac{1}{5} e^{5 x + 2} x - \frac{1}{25} e^{5 x + 2} + C

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What is the integral of x*e^{5x+2} ?
The integral of x*e^{5x+2} is 1/5 e^{5x+2}x-1/25 e^{5x+2}+C