What is the integral of (3x-2)e^{3x} ?

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

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integral of (3x-2)e^{3x}

\int (3 x - 2) e^{3 x} d x

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

Solution steps

\int (3 x - 2) e^{3 x} d x

Expand

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

= \int 3 e^{3 x} x - 2 e^{3 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 3 e^{3 x} x d x - \int 2 e^{3 x} d x

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

\int 2 e^{3 x} d x = \frac{2}{3} e^{3 x}

= e^{3 x} x - \frac{1}{3} e^{3 x} - \frac{2}{3} e^{3 x}

Simplify

e^{3 x} x - \frac{1}{3} e^{3 x} - \frac{2}{3} e^{3 x} : e^{3 x} x - e^{3 x}

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

Add a constant to the solution

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

a re a x^{6}, [0, 1]

\int \frac{x}{x + 23} d x

\int (sin (x))^{2} (cos (x))^{4} d x

- y^{^{'}} - y = e^{x}

n = 1 \sum \infty - 1

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