What is the integral of cos^2(x)-1 ?

The integral of cos^2(x)-1 is -1/2 x+1/4 sin(2x)+C

Popular >

integral of cos^2(x)-1

\int cos^{2} (x) - 1 d x

- \frac{1}{2} x + \frac{1}{4} sin (2 x) + C

Solution steps

\int cos^{2} (x) - 1 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

= \int cos^{2} (x) d x - \int 1 d x

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

\int 1 d x = x

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

Simplify

\frac{1}{2} (x + \frac{1}{2} sin (2 x)) - x : - \frac{1}{2} x + \frac{1}{4} sin (2 x)

= - \frac{1}{2} x + \frac{1}{4} sin (2 x)

Add a constant to the solution

= - \frac{1}{2} x + \frac{1}{4} sin (2 x) + C

\int 8 d x

\int \frac{18 x ^{2}}{3 x ^{3} + 4} d x

\int x^{\frac{1}{3}} + 4 d x

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

\int \frac{x ^{5}}{2} + 8 x^{4} + 2 x^{3} d x

What is the integral of cos^2(x)-1 ?
The integral of cos^2(x)-1 is -1/2 x+1/4 sin(2x)+C