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

The integral of (x+2)e^{3x} is 1/3 e^{3x}x+5/9 e^{3x}+C

Popular >

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

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

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

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} e^{3 x} (x + 2) - \int \frac{1}{3} e^{3 x} d x

= \frac{1}{3} e^{3 x} (x + 2) - \int \frac{1}{3} e^{3 x} d x

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

= \frac{1}{3} e^{3 x} (x + 2) - \frac{1}{9} e^{3 x}

Simplify

\frac{1}{3} e^{3 x} (x + 2) - \frac{1}{9} e^{3 x} : \frac{1}{3} e^{3 x} x + \frac{5}{9} e^{3 x}

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

Add a constant to the solution

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

\int e^{x} 3 e^{x} + 2 d x

\int \frac{- 7 x ^{3}}{x ^{2} + 9} d x

\int \frac{x - x}{x ^{2}} d x

\int \frac{( ln ( x ) - 1 ) ln ( x )}{x} d x

\int x^{\frac{1}{2}} - 3 x^{- \frac{1}{2}} d x

What is the integral of (x+2)e^{3x} ?
The integral of (x+2)e^{3x} is 1/3 e^{3x}x+5/9 e^{3x}+C