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

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

\int (2 x + 4) \cdot 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

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

\frac{d}{d x} (x + x^{2} + x^{3})

\frac{\partial}{\partial x} (sin (y) - cos (x))

y = \frac{1}{x}, y = \frac{1}{x ^{2}}, x = 5

\frac{d}{d x} (- 3 x^{4} + 2 y^{2})

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