What is the integral of sin^{27}(x)cos(x) ?

The integral of sin^{27}(x)cos(x) is (sin^{28}(x))/(28)+C

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integral of sin^{27}(x)cos(x)

\int sin^{27} (x) cos (x) d x

\frac{sin ^{28} ( x )}{28} + C

Solution steps

\int sin^{27} (x) cos (x) d x

Apply u-substitution

: \int u^{27} d u

= \int u^{27} d u

Apply the Power Rule

: \frac{u ^{28}}{28}

= \frac{u ^{28}}{28}

Substitute back

u = sin (x)

= \frac{sin ^{28} ( x )}{28}

Add a constant to the solution

= \frac{sin ^{28} ( x )}{28} + C

f (x) = e^{x} cos (x), at x = 0

\int 4 csc (x) cot (x) d x

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\int e^{7 x} sin (4 x) d x

f (x) = 1 + e^{2 x}

What is the integral of sin^{27}(x)cos(x) ?
The integral of sin^{27}(x)cos(x) is (sin^{28}(x))/(28)+C