What is the integral of (6x+3)e-2x ?

The integral of (6x+3)e-2x is e(3x^2+3x)-x^2+C

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integral of (6x+3)e-2x

\int (6 x + 3) e - 2 x d x

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

Solution steps

\int (6 x + 3) e - 2 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int (6 x + 3) e d x - \int 2 x d x

\int (6 x + 3) e d x = e (3 x^{2} + 3 x)

\int 2 x d x = x^{2}

= e (3 x^{2} + 3 x) - x^{2}

Add a constant to the solution

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

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What is the integral of (6x+3)e-2x ?
The integral of (6x+3)e-2x is e(3x^2+3x)-x^2+C