What is the integral of (2x+5)e^{2x+5} ?

The integral of (2x+5)e^{2x+5} is e^{2x+5}x+2e^{2x+5}+C

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integral of (2x+5)e^{2x+5}

\int (2 x + 5) e^{2 x + 5} d x

e^{2 x + 5} x + 2 e^{2 x + 5} + C

Solution steps

\int (2 x + 5) e^{2 x + 5} d x

Apply Integration By Parts

: e^{2 x + 5} x + \frac{5}{2} e^{2 x + 5} - \int e^{2 x + 5} d x

= e^{2 x + 5} x + \frac{5}{2} e^{2 x + 5} - \int e^{2 x + 5} d x

\int e^{2 x + 5} d x = \frac{1}{2} e^{2 x + 5}

= e^{2 x + 5} x + \frac{5}{2} e^{2 x + 5} - \frac{1}{2} e^{2 x + 5}

Add similar elements:

\frac{5}{2} e^{2 x + 5} - \frac{1}{2} e^{2 x + 5} = 2 e^{2 x + 5}

= e^{2 x + 5} x + 2 e^{2 x + 5}

Add a constant to the solution

= e^{2 x + 5} x + 2 e^{2 x + 5} + C

- \frac{9}{2} x^{2} + 3 x + 3

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 5})

\int cos^{3} (x s i) n^{2} x d x

\frac{\partial}{\partial x} (- 3 \cdot x^{2} + 28)

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

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