What is the integral of (2x+4)e^{2x+4} ?

The integral of (2x+4)e^{2x+4} is e^{2x+4}x+3/2 e^{2x+4}+C

Popular >

integral of (2x+4)e^{2x+4}

\int (2 x + 4) e^{2 x + 4} d x

e^{2 x + 4} x + \frac{3}{2} e^{2 x + 4} + C

Solution steps

\int (2 x + 4) e^{2 x + 4} d x

Apply Integration By Parts

: e^{2 x + 4} (x + 2) - \int e^{2 x + 4} d x

= e^{2 x + 4} (x + 2) - \int e^{2 x + 4} d x

\int e^{2 x + 4} d x = \frac{1}{2} e^{2 x + 4}

= e^{2 x + 4} (x + 2) - \frac{1}{2} e^{2 x + 4}

Simplify

e^{2 x + 4} (x + 2) - \frac{1}{2} e^{2 x + 4} : e^{2 x + 4} x + \frac{3}{2} e^{2 x + 4}

= e^{2 x + 4} x + \frac{3}{2} e^{2 x + 4}

Add a constant to the solution

= e^{2 x + 4} x + \frac{3}{2} e^{2 x + 4} + C

\frac{d}{d x} ([x + (x + sin^{2} (x))^{6}]^{3})

\int (2 x - 1)^{4} d x

\int \frac{1}{4 x ^{2} - 25} d x

\frac{d y}{d x} = \frac{9 x + 4 y}{9 x + 4 y + 4}

\int_{60}^{v} \frac{1}{- 0.4 v ^{3}} d v

What is the integral of (2x+4)e^{2x+4} ?
The integral of (2x+4)e^{2x+4} is e^{2x+4}x+3/2 e^{2x+4}+C