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

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integral of (e^x+2)^2

integral

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

\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{2 - x}{1 - x}

\frac{tan ( x )}{( 1 + cos ^{4} ( x ) )}

2 e^{- 2 x}

\frac{1}{( x )}

\frac{x ^{2}}{( 1 + x ^{3} )}

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