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

The integral of sin^2(5x) is 1/2 (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 sin^2(5x)

integral

sin^{2} (5 x)

\frac{1}{2} (x - \frac{1}{10} sin (10 x)) + C

Solution steps

\int sin^{2} (5 x) d x

Rewrite using trig identities

= \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

= \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

= \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)

= \frac{1}{2} (x - \frac{1}{10} sin (10 x))

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{10} sin (10 x)) + C

1 - sin^{2} (x)

1 - ∣ x ∣

(1 - x)^{3}

e^{2} x^{2}

\frac{1}{( 2 x + 1 ) ^{3}}

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