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) 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

\frac{\partial}{\partial x} (90 - 4 x^{2} - 1 y^{2})

y^{^{'}} = \frac{t ^{2}}{y} (1 + t^{3})

\int_{0}^{13} 8 x d x

(3 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

- 10 x^{2} y + y^{^{'}} = 5 x^{2}

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