What is the integral of cos(x)*cos(x) ?

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

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integral of cos(x)*cos(x)

\int cos (x) \cdot cos (x) d x

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

Solution steps

\int cos (x) cos (x) d x

Simplify

cos (x) cos (x) : cos^{2} (x)

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

Rewrite using trig identities

= \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

= \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

= \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)

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

Add a constant to the solution

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

\int tan^{8} (x) sec^{4} (x) d x

y = 4 - x^{2}, (4, - 12)

\int \frac{6 x}{( 9 x ^{2} - 4 ) ^{3}} d x

\frac{\partial}{\partial x} x y \cdot e^{(\frac{( - 5 x ^{2} + 5 y ^{2} )}{2} + 1)}

\frac{d y}{d x} = y^{2} (6 - 2 x)

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