What is the integral of 18cos^2(89x) ?

The integral of 18cos^2(89x) is 9(x+1/178 sin(178x))+C

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integral of 18cos^2(89x)

\int 18 cos^{2} (89 x) d x

9 (x + \frac{1}{178} sin (178 x)) + C

Solution steps

\int 18 cos^{2} (89 x) d x

Take the constant out:

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

= 18 \cdot \int cos^{2} (89 x) d x

Rewrite using trig identities

= 18 \cdot \int \frac{1}{2} (1 + cos (178 x)) d x

Take the constant out:

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

= 18 \cdot \frac{1}{2} \cdot \int 1 + cos (178 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

= 18 \cdot \frac{1}{2} (\int 1 d x + \int cos (178 x) d x)

\int 1 d x = x

\int cos (178 x) d x = \frac{1}{178} sin (178 x)

= 18 \cdot \frac{1}{2} (x + \frac{1}{178} sin (178 x))

Simplify

18 \cdot \frac{1}{2} (x + \frac{1}{178} sin (178 x)) : 9 (x + \frac{1}{178} sin (178 x))

= 9 (x + \frac{1}{178} sin (178 x))

Add a constant to the solution

= 9 (x + \frac{1}{178} sin (178 x)) + C

arctan (t)

\int (16 x + 7) d x

\frac{d}{d x} ((x^{\frac{2}{3}}) (x - 4))

\int (9 x - 16)^{3} d x

\frac{d}{d x} (ln (\frac{3 x + 4}{3 x - 4}))

What is the integral of 18cos^2(89x) ?
The integral of 18cos^2(89x) is 9(x+1/178 sin(178x))+C