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

The integral of (e^x+2)^2 is 1/2 e^{2x}+4e^x+4x+C

Popular >

integral of (e^x+2)^2

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

\frac{1}{2} e^{2 x} + 4 e^{x} + 4 x + C

Solution steps

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

Expand

(e^{x} + 2)^{2} : e^{2 x} + 4 e^{x} + 4

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

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

\int 4 e^{x} d x = 4 e^{x}

\int 4 d x = 4 x

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (- 5 y^{3} sin (5 x))

y = \frac{2}{x}, y = 8 x, y = \frac{1}{8} x

\int_{2}^{\infty} \frac{1}{ln ( x )} d x

x \to \infty lim (- \frac{1}{2} e^{- x^{2}})

\int_{1}^{2} cos (\frac{π x}{3}) d x

What is the integral of (e^x+2)^2 ?
The integral of (e^x+2)^2 is 1/2 e^{2x}+4e^x+4x+C