What is the integral of 5sin^4(r)cos(r) ?

The integral of 5sin^4(r)cos(r) is sin^5(r)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5sin^4(r)cos(r)

\int 5 sin^{4} (r) cos (r) d r

sin^{5} (r) + C

Solution steps

\int 5 sin^{4} (r) cos (r) d r

Take the constant out:

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

= 5 \cdot \int sin^{4} (r) cos (r) d r

Apply u-substitution

: \int u^{4} d u

= 5 \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 5 \cdot \frac{u ^{5}}{5}

Substitute back

u = sin (r)

= 5 \cdot \frac{sin ^{5} ( r )}{5}

Simplify

5 \cdot \frac{sin ^{5} ( r )}{5} : sin^{5} (r)

= sin^{5} (r)

Add a constant to the solution

= sin^{5} (r) + C

\frac{e ^{x}}{x ^{2}}

\frac{d}{d x} ((x - a)^{3} (x - b))

\frac{\partial}{\partial y} (x^{4} + 3 x^{2} y)

3 x^{2} cos (3 x)

\frac{\partial}{\partial x} (5 x y - 3 x^{2} y)

What is the integral of 5sin^4(r)cos(r) ?
The integral of 5sin^4(r)cos(r) is sin^5(r)+C