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

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

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integral of sin^6(x)cos(x)

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

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

Solution steps

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

Apply u-substitution

= \int u^{6} d u

Apply the Power Rule

= \frac{u ^{7}}{7}

Substitute back

u = sin (x)

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

Add a constant to the solution

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

d er i v a t i v e x^{n}

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\int sin (x) cos (k x) d x

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