What is the integral of sin^3(y)cos(y) ?

The integral of sin^3(y)cos(y) is (sin^4(y))/4+C

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integral of sin^3(y)cos(y)

\int sin^{3} (y) cos (y) d y

\frac{sin ^{4} ( y )}{4} + C

Solution steps

\int sin^{3} (y) cos (y) d y

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = sin (y)

= \frac{sin ^{4} ( y )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( y )}{4} + C

f (x) = (1 + x)^{5}

g (x) = (1 - 3 x)

\frac{d}{d x} (8 - 3 x)

\frac{\partial}{\partial x} (x^{4} + y^{4} - 32 x + 4 y + 4)

\frac{d}{d x} (f (x) (x g (x)))

What is the integral of sin^3(y)cos(y) ?
The integral of sin^3(y)cos(y) is (sin^4(y))/4+C