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

The integral of 9cos^2(x) is 9/2 (x+1/2 sin(2x))+C

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integral of 9cos^2(x)

integral

9 cos^{2} (x)

\frac{9}{2} (x + \frac{1}{2} sin (2 x)) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int cos^{2} (x) d x

Rewrite using trig identities

= 9 \cdot \int \frac{1 + cos ( 2 x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \frac{1}{2} \cdot \int 1 + 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

= 9 \cdot \frac{1}{2} (\int 1 d x + \int cos (2 x) d x)

\int 1 d x = x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

= 9 \cdot \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Simplify

9 \cdot \frac{1}{2} (x + \frac{1}{2} sin (2 x)) : \frac{9}{2} (x + \frac{1}{2} sin (2 x))

= \frac{9}{2} (x + \frac{1}{2} sin (2 x))

Add a constant to the solution

= \frac{9}{2} (x + \frac{1}{2} sin (2 x)) + C

x lo g_{10} (x^{2} + 5)

f (x) = (x^{2} + x + 1)^{\frac{1}{2}}

\frac{( x ^{3} - 1 )}{( x - 1 )}

\frac{( x ^{4} - 4 x ^{2} + x + 1 )}{( x ^{2} - 4 )}

\frac{2 y}{x}

What is the integral of 9cos^2(x) ?
The integral of 9cos^2(x) is 9/2 (x+1/2 sin(2x))+C