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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2cos^2(x)-1)

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

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

Solution steps

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

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

\int 1 d x = x

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

Simplify

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

Add a constant to the solution

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

\int \frac{x ^{2}}{6 + x} d x

\int 10 x - 4 x^{3} d x

\int k x k x^{2} + 10 d x

\int (16 y^{3} - 3 y^{2} + 2) d y

\int \frac{x ^{4} - x ^{3}}{4 x ^{5} - 5 x ^{4}} d x

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