What is the integral of (sin(x))^{1/2}cos(x) ?

The integral of (sin(x))^{1/2}cos(x) is 2/3 sin^{3/2}(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(x))^{1/2}cos(x)

\int (sin (x))^{\frac{1}{2}} cos (x) d x

\frac{2}{3} sin^{\frac{3}{2}} (x) + C

Solution steps

\int sin^{\frac{1}{2}} (x) cos (x) d x

Apply u-substitution

: \int u^{\frac{1}{2}} d u

= \int u^{\frac{1}{2}} d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = sin (x)

= \frac{2}{3} sin^{\frac{3}{2}} (x)

Add a constant to the solution

= \frac{2}{3} sin^{\frac{3}{2}} (x) + C

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = x^{2} - 4 x

y \cdot y^{^{'}} + 36 x = 0

y = x, y = \frac{x}{2}

\frac{d}{d x} (a e^{- 2 x})

\frac{d y}{d x}, 4 x^{2} y^{7} - 2 x = x^{5} + 4 y^{3}

What is the integral of (sin(x))^{1/2}cos(x) ?
The integral of (sin(x))^{1/2}cos(x) is 2/3 sin^{3/2}(x)+C