What is the integral of cos^1(x)sin^5(x) ?

The integral of cos^1(x)sin^5(x) is (sin^6(x))/6+C

Popular >

integral of cos^1(x)sin^5(x)

\int cos^{1} (x) sin^{5} (x) d x

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

Solution steps

\int cos^{1} (x) sin^{5} (x) d x

Simplify

sin^{5} (x) : sin^{4} (x) sin (x)

= \int cos^{1} (x) sin^{4} (x) sin (x) d x

Simplify

cos^{1} (x) sin^{4} (x) sin (x) : sin^{5} (x) cos (x)

= \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

\int - sec^{2} (\frac{9 x}{7}) d x

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

\int [x - \frac{5}{( 3 x + 5 ) ^{2}}] d x

\int (3 - 2 x) \cdot sin (5 - 4 x) d x

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

What is the integral of cos^1(x)sin^5(x) ?
The integral of cos^1(x)sin^5(x) is (sin^6(x))/6+C