What is the integral of sin^5(x/7)cos(x/7) ?

The integral of sin^5(x/7)cos(x/7) is 7/6 sin^6(x/7)+C

Popular >

integral of sin^5(x/7)cos(x/7)

\int sin^{5} (\frac{x}{7}) cos (\frac{x}{7}) d x

\frac{7}{6} sin^{6} (\frac{x}{7}) + C

Solution steps

\int sin^{5} (\frac{x}{7}) cos (\frac{x}{7}) d x

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{5}{6} u^{\frac{6}{5}}

= \frac{7}{5} \cdot \frac{5}{6} u^{\frac{6}{5}}

Substitute back

u = sin^{5} (\frac{x}{7})

= \frac{7}{5} \cdot \frac{5}{6} (sin^{5} (\frac{x}{7}))^{\frac{6}{5}}

Simplify

\frac{7}{5} \cdot \frac{5}{6} (sin^{5} (\frac{x}{7}))^{\frac{6}{5}} : \frac{7}{6} sin^{6} (\frac{x}{7})

= \frac{7}{6} sin^{6} (\frac{x}{7})

Add a constant to the solution

= \frac{7}{6} sin^{6} (\frac{x}{7}) + C

x \to 1 + lim (x^{\frac{2}{x - 1}})

\frac{d ^{2}}{d x ^{2}} (\frac{( x - 3 ) ( x ^{2} + 3 x + 9 )}{x ^{3}})

\int - \frac{1}{5} cos (5 x) d x

\int \frac{( 2 x ^{2} + x + 4 )}{x ^{3} + 4 x ^{2}} d x

\frac{d}{d x} (x^{3} + 6)

What is the integral of sin^5(x/7)cos(x/7) ?
The integral of sin^5(x/7)cos(x/7) is 7/6 sin^6(x/7)+C