What is the integral of t^2cos(1-t^3) ?

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

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integral of t^2cos(1-t^3)

\int t^{2} cos (1 - t^{3}) d t

- \frac{1}{3} sin (1 - t^{3}) + C

Solution steps

\int t^{2} cos (1 - t^{3}) d t

Apply u-substitution

= \int - \frac{cos ( u )}{3} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= - \frac{1}{3} sin (u)

Substitute back

u = 1 - t^{3}

= - \frac{1}{3} sin (1 - t^{3})

Add a constant to the solution

= - \frac{1}{3} sin (1 - t^{3}) + C

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