What is the integral of (4cos^2(x)) ?

The integral of (4cos^2(x)) is 2x+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 (4cos^2(x))

\int (4 cos^{2} (x)) d x

2 x + sin (2 x) + C

Solution steps

\int 4 cos^{2} (x) d x

Take the constant out:

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

= 4 \cdot \int cos^{2} (x) d x

Rewrite using trig identities

= 4 \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

= 4 \cdot \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

= 4 \cdot \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)

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

Simplify

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

= 2 x + sin (2 x)

Add a constant to the solution

= 2 x + sin (2 x) + C

e^{e^{- x}}

\int cos (3 π t) d t

\int 1 - \frac{3}{y} d y

f (x) = - 8 sin (x)

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 9 y^{3})

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