What is the integral of (3x+1)e^x ?

The integral of (3x+1)e^x is 3e^xx-2e^x+C

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integral of (3x+1)e^x

\int (3 x + 1) e^{x} d x

3 e^{x} x - 2 e^{x} + C

Solution steps

\int (3 x + 1) e^{x} d x

Apply Integration By Parts

: (3 x + 1) e^{x} - \int 3 e^{x} d x

= (3 x + 1) e^{x} - \int 3 e^{x} d x

\int 3 e^{x} d x = 3 e^{x}

= (3 x + 1) e^{x} - 3 e^{x}

Simplify

(3 x + 1) e^{x} - 3 e^{x} : 3 e^{x} x - 2 e^{x}

= 3 e^{x} x - 2 e^{x}

Add a constant to the solution

= 3 e^{x} x - 2 e^{x} + C

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