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

The integral of (2+2cos(x))^2 is 6x+8sin(x)+sin(2x)+C

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integral of (2+2cos(x))^2

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

6 x + 8 sin (x) + sin (2 x) + C

Solution steps

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

Expand

(2 + 2 cos (x))^{2} : 4 + 8 cos (x) + 4 cos^{2} (x)

= \int 4 + 8 cos (x) + 4 cos^{2} (x) 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 4 d x + \int 8 cos (x) d x + \int 4 cos^{2} (x) d x

\int 4 d x = 4 x

\int 8 cos (x) d x = 8 sin (x)

\int 4 cos^{2} (x) d x = 2 x + sin (2 x)

= 4 x + 8 sin (x) + 2 x + sin (2 x)

Simplify

= 6 x + 8 sin (x) + sin (2 x)

Add a constant to the solution

= 6 x + 8 sin (x) + sin (2 x) + C

\int_{0}^{π} 9 sin (x) d x

\frac{d}{d x} (\frac{x ^{12}}{x ^{2}})

y^{^{'}} = x^{2} \cdot (1 + y)

n = 1 \sum \infty n (\frac{1}{2})^{n}

\int cos (3 x) e^{2 x} d x

What is the integral of (2+2cos(x))^2 ?
The integral of (2+2cos(x))^2 is 6x+8sin(x)+sin(2x)+C