What is the integral of xe^{3x+5} ?

The integral of xe^{3x+5} is 1/3 e^{3x+5}x-1/9 e^{3x+5}+C

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integral of xe^{3x+5}

\int x e^{3 x + 5} d x

\frac{1}{3} e^{3 x + 5} x - \frac{1}{9} e^{3 x + 5} + C

Solution steps

\int x e^{3 x + 5} d x

Apply Integration By Parts

= \frac{1}{3} e^{3 x + 5} x - \int \frac{1}{3} e^{3 x + 5} d x

\int \frac{1}{3} e^{3 x + 5} d x = \frac{1}{9} e^{3 x + 5}

= \frac{1}{3} e^{3 x + 5} x - \frac{1}{9} e^{3 x + 5}

Add a constant to the solution

= \frac{1}{3} e^{3 x + 5} x - \frac{1}{9} e^{3 x + 5} + C

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What is the integral of xe^{3x+5} ?
The integral of xe^{3x+5} is 1/3 e^{3x+5}x-1/9 e^{3x+5}+C