What is the integral of sin^6(x) ?

The integral of sin^6(x) is -(cos(x)sin^5(x))/6+5/6 (-1/4 sin^3(x)cos(x)+3/8 (x-1/2 sin(2x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin^6(x)

integral

sin^{6} (x)

- \frac{cos ( x ) sin ^{5} ( x )}{6} + \frac{5}{6} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x))) + C

Solution steps

\int sin^{6} (x) d x

Apply Integral Reduction

= - \frac{cos ( x ) sin ^{5} ( x )}{6} + \frac{5}{6} \cdot \int sin^{4} (x) d x

\int sin^{4} (x) d x = - \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x))

= - \frac{cos ( x ) sin ^{5} ( x )}{6} + \frac{5}{6} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x)))

Add a constant to the solution

= - \frac{cos ( x ) sin ^{5} ( x )}{6} + \frac{5}{6} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x))) + C

(e^{t})^{2}

e^{\frac{1}{x}} x

\frac{( x - 1 ) ^{2}}{x ^{2}}

\frac{t}{6}

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

What is the integral of sin^6(x) ?
The integral of sin^6(x) is -(cos(x)sin^5(x))/6+5/6 (-1/4 sin^3(x)cos(x)+3/8 (x-1/2 sin(2x)))+C