What is the integral of tsin(4)t^2 ?

The integral of tsin(4)t^2 is 1/4 sin(4)t^4+C

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integral of tsin(4)t^2

\int t sin (4) t^{2} d t

\frac{1}{4} sin (4) t^{4} + C

Solution steps

\int t sin (4) t^{2} d t

Take the constant out:

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

= sin (4) \cdot \int t t^{2} d t

Simplify

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

= sin (4) \cdot \int t^{3} d t

Apply the Power Rule

: \frac{t ^{4}}{4}

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

Simplify

sin (4) \frac{t ^{4}}{4} : \frac{1}{4} sin (4) t^{4}

= \frac{1}{4} sin (4) t^{4}

Add a constant to the solution

= \frac{1}{4} sin (4) t^{4} + C

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What is the integral of tsin(4)t^2 ?
The integral of tsin(4)t^2 is 1/4 sin(4)t^4+C