What is the integral of cos^2(15x) ?

The integral of cos^2(15x) is 1/2 (x+1/30 sin(30x))+C

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integral of cos^2(15x)

\int cos^{2} (15 x) d x

\frac{1}{2} (x + \frac{1}{30} sin (30 x)) + C

Solution steps

\int cos^{2} (15 x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 + cos (30 x)) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int 1 + cos (30 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

= \frac{1}{2} (\int 1 d x + \int cos (30 x) d x)

\int 1 d x = x

\int cos (30 x) d x = \frac{1}{30} sin (30 x)

= \frac{1}{2} (x + \frac{1}{30} sin (30 x))

Add a constant to the solution

= \frac{1}{2} (x + \frac{1}{30} sin (30 x)) + C

\int \frac{2}{5 x - 1} d x

\frac{\partial}{\partial y} (3 x^{2} + y^{2})

\frac{d}{d x} (6 x^{7})

\frac{d}{d x} (3 a x + b x^{3})

\frac{\partial}{\partial x} (3 x^{2} + 5 x y - 7 y^{2} + 1)

What is the integral of cos^2(15x) ?
The integral of cos^2(15x) is 1/2 (x+1/30 sin(30x))+C