What is the integral of 8sin(x)cos(x) ?

The integral of 8sin(x)cos(x) is 4sin^2(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 8sin(x)cos(x)

\int 8 sin (x) cos (x) d x

4 sin^{2} (x) + C

Solution steps

\int 8 sin (x) cos (x) d x

Take the constant out:

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

= 8 \cdot \int sin (x) cos (x) d x

Apply u-substitution

= 8 \cdot \int u d u

Apply the Power Rule

= 8 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 8 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

8 \cdot \frac{sin ^{2} ( x )}{2} : 4 sin^{2} (x)

= 4 sin^{2} (x)

Add a constant to the solution

= 4 sin^{2} (x) + C

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