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

The integral of sin^5(x)*cos(x) is (sin^6(x))/6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int sin^{5} (x) \cdot cos (x) d x

\frac{sin ^{6} ( x )}{6} + C

Solution steps

\int sin^{5} (x) cos (x) d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = sin (x)

= \frac{sin ^{6} ( x )}{6}

Add a constant to the solution

= \frac{sin ^{6} ( x )}{6} + C

\frac{d}{d x} (\frac{sin ( π ) x}{ln ( x )})

\int_{- 3}^{0} x^{2} e^{x^{3} + 27} d x

\frac{d}{d z} (z^{2} e^{z})

f (x) = \frac{1}{( 1 + x )}

\frac{d}{d x} (4 ln ∣ x - e^{x} ∣)

What is the integral of sin^5(x)*cos(x) ?
The integral of sin^5(x)*cos(x) is (sin^6(x))/6+C