What is the integral of 8cos^2(5x) ?

The integral of 8cos^2(5x) is 4(x+1/10 sin(10x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 8cos^2(5x)

\int 8 cos^{2} (5 x) d x

4 (x + \frac{1}{10} sin (10 x)) + C

Solution steps

\int 8 cos^{2} (5 x) d x

Take the constant out:

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

= 8 \cdot \int cos^{2} (5 x) d x

Rewrite using trig identities

= 8 \cdot \int \frac{1}{2} (1 + cos (10 x)) d x

Take the constant out:

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

= 8 \cdot \frac{1}{2} \cdot \int 1 + cos (10 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

= 8 \cdot \frac{1}{2} (\int 1 d x + \int cos (10 x) d x)

\int 1 d x = x

\int cos (10 x) d x = \frac{1}{10} sin (10 x)

= 8 \cdot \frac{1}{2} (x + \frac{1}{10} sin (10 x))

Simplify

8 \cdot \frac{1}{2} (x + \frac{1}{10} sin (10 x)) : 4 (x + \frac{1}{10} sin (10 x))

= 4 (x + \frac{1}{10} sin (10 x))

Add a constant to the solution

= 4 (x + \frac{1}{10} sin (10 x)) + C

\frac{d}{d x} (\frac{5 ^{x} + 2}{5 ^{x} + 1})

y = - 8 + 5 x

\int \frac{14}{1 - cos ( 2 x )} d x

\int 6 x^{2} y - 2 x d y

\frac{\partial}{\partial x} (y x^{2} + x y^{2} + y z^{2})

What is the integral of 8cos^2(5x) ?
The integral of 8cos^2(5x) is 4(x+1/10 sin(10x))+C