What is the integral of (x+2)e^{7x} ?

The integral of (x+2)e^{7x} is 1/7 e^{7x}x+13/49 e^{7x}+C

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integral of (x+2)e^{7x}

\int (x + 2) e^{7 x} d x

\frac{1}{7} e^{7 x} x + \frac{13}{49} e^{7 x} + C

Solution steps

\int (x + 2) e^{7 x} d x

Apply Integration By Parts

: \frac{1}{7} e^{7 x} (x + 2) - \int \frac{1}{7} e^{7 x} d x

= \frac{1}{7} e^{7 x} (x + 2) - \int \frac{1}{7} e^{7 x} d x

\int \frac{1}{7} e^{7 x} d x = \frac{1}{49} e^{7 x}

= \frac{1}{7} e^{7 x} (x + 2) - \frac{1}{49} e^{7 x}

Simplify

\frac{1}{7} e^{7 x} (x + 2) - \frac{1}{49} e^{7 x} : \frac{1}{7} e^{7 x} x + \frac{13}{49} e^{7 x}

= \frac{1}{7} e^{7 x} x + \frac{13}{49} e^{7 x}

Add a constant to the solution

= \frac{1}{7} e^{7 x} x + \frac{13}{49} e^{7 x} + C

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What is the integral of (x+2)e^{7x} ?
The integral of (x+2)e^{7x} is 1/7 e^{7x}x+13/49 e^{7x}+C