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

The integral of sin^2(5x)cos^2(5x) is 1/8 (x-1/20 sin(20x))+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)cos^2(5x)

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

\frac{1}{8} (x - \frac{1}{20} sin (20 x)) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{8} (1 - cos (20 x)) d x

Take the constant out:

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

= \frac{1}{8} \cdot \int 1 - cos (20 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}{8} (\int 1 d x - \int cos (20 x) d x)

\int 1 d x = x

\int cos (20 x) d x = \frac{1}{20} sin (20 x)

= \frac{1}{8} (x - \frac{1}{20} sin (20 x))

Add a constant to the solution

= \frac{1}{8} (x - \frac{1}{20} sin (20 x)) + C

(t + 1)^{\frac{2}{3}} (3 t^{2} - 2)^{3}

\frac{d}{d x} (\frac{e ^{x}}{1 + e ^{x}})

3 e^{5 x} \frac{d y}{d x} = - 25 \frac{x}{y ^{2}}

\int 2 tan (θ) d θ

\int 4 sin^{3} (x co) s^{5} x d x

What is the integral of sin^2(5x)cos^2(5x) ?
The integral of sin^2(5x)cos^2(5x) is 1/8 (x-1/20 sin(20x))+C