What is the integral of 9+12cos(x)+4cos^2(x) ?

The integral of 9+12cos(x)+4cos^2(x) is 11x+12sin(x)+sin(2x)+C

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integral of 9+12cos(x)+4cos^2(x)

\int 9 + 12 cos (x) + 4 cos^{2} (x) d x

11 x + 12 sin (x) + sin (2 x) + C

Solution steps

\int 9 + 12 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 9 d x + \int 12 cos (x) d x + \int 4 cos^{2} (x) d x

\int 9 d x = 9 x

\int 12 cos (x) d x = 12 sin (x)

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

= 9 x + 12 sin (x) + 2 x + sin (2 x)

Simplify

= 11 x + 12 sin (x) + sin (2 x)

Add a constant to the solution

= 11 x + 12 sin (x) + sin (2 x) + C

x 4

f^{^{'}} (x) = 1.9181 \cdot x^{2} + 177.69 \cdot x - 0.4 \cdot x^{3}

(8 - 9 x) (8 + 9 x)

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

n = 1 \sum \infty \frac{4}{n ^{3}}

What is the integral of 9+12cos(x)+4cos^2(x) ?
The integral of 9+12cos(x)+4cos^2(x) is 11x+12sin(x)+sin(2x)+C