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

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

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integral of t^2cos(t^3)

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

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

Solution steps

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

Apply u-substitution

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

= \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 = t^{3}

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

Add a constant to the solution

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

x \to 0 lim (\frac{∣ x ∣}{x} - 1)

\frac{d}{d x} (\frac{3}{1 + x})

y^{^{'}} - 2 y = x y^{3}, y (0) = 22

(x \cdot y) d x + x d y = 0

x \to 0 lim (\frac{sin ( \frac{1}{x} )}{x})

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