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

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

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integral of cos(x)os(x)

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

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

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Rewrite using trig identities

= d \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

= d \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

= d \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)

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

Add a constant to the solution

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

\int \frac{x ^{2} + 2 x - 1}{x ^{3} - 27} d x

\int x^{3} + 2 x^{2} - x + \frac{2}{x ^{2}} d x

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

\int \frac{7 e ^{7} x}{x} d x

\int e^{x + 2} d x

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