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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(5x)cos(5x)

\int sin (5 x) cos (5 x) d x

- \frac{1}{10} cos^{2} (5 x) + C

Solution steps

\int sin (5 x) cos (5 x) d x

Apply u-substitution

: \int - \frac{u}{5} d u

= \int - \frac{u}{5} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= - \frac{1}{5} \cdot \frac{u ^{2}}{2}

Substitute back

u = cos (5 x)

= - \frac{1}{5} \cdot \frac{cos ^{2} ( 5 x )}{2}

Simplify

- \frac{1}{5} \cdot \frac{cos ^{2} ( 5 x )}{2} : - \frac{1}{10} cos^{2} (5 x)

= - \frac{1}{10} cos^{2} (5 x)

Add a constant to the solution

= - \frac{1}{10} cos^{2} (5 x) + C

\int 2 \frac{1}{x} d x

\int e^{- 7 x} tan (e^{- 7 x}) d x

x y^{^{'}} + 2 y ln (x) = 3

\int_{1}^{3} \frac{x ^{2} + 8}{4 x - x ^{2}} d x

y^{^{'}} = x y

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