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

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

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

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

- \frac{cos ^{6} ( x )}{6} + C

Solution steps

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

Apply u-substitution

: \int - u^{5} d u

= \int - u^{5} d u

Take the constant out:

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

= - \int u^{5} d u

Apply the Power Rule

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

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

Substitute back

u = cos (x)

= - \frac{cos ^{6} ( x )}{6}

Add a constant to the solution

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

V (r) = \frac{4}{3} π r^{3}

0.04 x^{2} - 2 x + 6 x^{0.2}

\frac{d}{d x} (sin (ln (x^{3})))

\int \frac{1}{x ^{3} - x ^{2} - 9 x + 9} d x

f (x) = 2 x^{3} + 5

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