What is the integral of sin^3(m)tcos^2(m)t ?

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

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integral of sin^3(m)tcos^2(m)t

\int sin^{3} (m) t cos^{2} (m) t d t

\frac{t ^{3} sin ^{3} ( m ) cos ^{2} ( m )}{3} + C

Solution steps

\int sin^{3} (m) t cos^{2} (m) t d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos^{2} (m) sin^{3} (m) \cdot \int tt d t

Simplify

tt : t^{2}

= cos^{2} (m) sin^{3} (m) \cdot \int t^{2} d t

Apply the Power Rule

= cos^{2} (m) sin^{3} (m) \frac{t ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{t ^{3} sin ^{3} ( m ) cos ^{2} ( m )}{3}

Add a constant to the solution

= \frac{t ^{3} sin ^{3} ( m ) cos ^{2} ( m )}{3} + C

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