What is the integral of sin^{12}(x)cos(x) ?

The integral of sin^{12}(x)cos(x) is (sin^{13}(x))/(13)+C

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integral of sin^{12}(x)cos(x)

\int sin^{12} (x) cos (x) d x

\frac{sin ^{13} ( x )}{13} + C

Solution steps

\int sin^{12} (x) cos (x) d x

Apply u-substitution

: \int u^{12} d u

= \int u^{12} d u

Apply the Power Rule

: \frac{u ^{13}}{13}

= \frac{u ^{13}}{13}

Substitute back

u = sin (x)

= \frac{sin ^{13} ( x )}{13}

Add a constant to the solution

= \frac{sin ^{13} ( x )}{13} + C

x \to 0 lim ((1 + 5 x)^{\frac{2}{x}})

\frac{d y}{d x} = k_{1} (y - c_{1})

cos (X)

\frac{h ( x )}{x}

x^{3} y^{^{'''}} + 6 x^{2} y^{^{''}} + 7 x y^{^{'}} + y = 0

What is the integral of sin^{12}(x)cos(x) ?
The integral of sin^{12}(x)cos(x) is (sin^{13}(x))/(13)+C