What is the integral of sin^3(t)cos(t) ?

The integral of sin^3(t)cos(t) is (sin^4(t))/4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sin^3(t)cos(t)

\int sin^{3} (t) cos (t) d t

\frac{sin ^{4} ( t )}{4} + C

Solution steps

\int sin^{3} (t) cos (t) d t

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \frac{u ^{4}}{4}

Substitute back

u = sin (t)

= \frac{sin ^{4} ( t )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( t )}{4} + C

d er i v a t i v e \frac{1}{3} (y^{2} + 2)^{\frac{3}{2}}

\frac{d}{d x} (ln (2 ln (x)))

\frac{d}{d x} ((3 x + 1)^{4})

d er i v a t i v e \frac{1}{3 x}

\frac{d}{d x} (\frac{x - 3}{x + 3})

What is the integral of sin^3(t)cos(t) ?
The integral of sin^3(t)cos(t) is (sin^4(t))/4+C