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

The integral of (1+cos^2(x)) is 3/2 x+1/4 sin(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{3}{2} x + \frac{1}{4} sin (2 x) + C

Solution steps

\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

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

\int 1 d x = x

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

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

Simplify

x + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) : \frac{3}{2} x + \frac{1}{4} sin (2 x)

= \frac{3}{2} x + \frac{1}{4} sin (2 x)

Add a constant to the solution

= \frac{3}{2} x + \frac{1}{4} sin (2 x) + C

What is the integral of (1+cos^2(x)) ?
The integral of (1+cos^2(x)) is 3/2 x+1/4 sin(2x)+C