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

The integral of t^2sin(3)(t^3)cos(2)(t^3) is 1/9 sin(3)cos(2)t^9+C

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integral of t^2sin(3)(t^3)cos(2)(t^3)

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

\frac{1}{9} sin (3) cos (2) t^{9} + C

Solution steps

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

Take the constant out:

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

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

Simplify

t^{2} t^{3} t^{3} : t^{8}

= sin (3) cos (2) \cdot \int t^{8} d t

Apply the Power Rule

: \frac{t ^{9}}{9}

= sin (3) cos (2) \frac{t ^{9}}{9}

Simplify

sin (3) cos (2) \frac{t ^{9}}{9} : \frac{1}{9} sin (3) cos (2) t^{9}

= \frac{1}{9} sin (3) cos (2) t^{9}

Add a constant to the solution

= \frac{1}{9} sin (3) cos (2) t^{9} + C

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What is the integral of t^2sin(3)(t^3)cos(2)(t^3) ?
The integral of t^2sin(3)(t^3)cos(2)(t^3) is 1/9 sin(3)cos(2)t^9+C