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

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

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integral of t^2sin(t^3)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{sin ( u )}{3} d u

= \int \frac{sin ( 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 sin (u) d u

Use the common integral:

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

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

Substitute back

u = t^{3}

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

Simplify

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

Add a constant to the solution

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

\int (x - 1)^{10} (x + 3)^{2} d x

\int \frac{2 ^{x}}{5 ^{x}} d x

\frac{d}{d x} (\frac{3}{sin ( x ) + cos ( x )})

x \to 0 lim (cot (2 x))

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