What is the integral of sin^2(t)cos(t) ?

The integral of sin^2(t)cos(t) is (sin^3(t))/3+C

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integral of sin^2(t)cos(t)

\int sin^{2} (t) cos (t) d t

\frac{sin ^{3} ( t )}{3} + C

Solution steps

\int sin^{2} (t) cos (t) d t

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = sin (t)

= \frac{sin ^{3} ( t )}{3}

Add a constant to the solution

= \frac{sin ^{3} ( t )}{3} + C

x \to 3 lim (5 x + 4)

\int 0.0025 x - 0.075 d x

x \to 3 π lim (csc (x))

y^{^{'}} - 6 y = 0, y (2) = 4

\frac{d}{d x} (A e^{- x})

What is the integral of sin^2(t)cos(t) ?
The integral of sin^2(t)cos(t) is (sin^3(t))/3+C