What is the integral of x^2cos(1-1/4 x^3) ?

The integral of x^2cos(1-1/4 x^3) is -4/3 sin(1-1/4 x^3)+C

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integral of x^2cos(1-1/4 x^3)

\int x^{2} cos (1 - \frac{1}{4} x^{3}) d x

- \frac{4}{3} sin (1 - \frac{1}{4} x^{3}) + C

Solution steps

\int x^{2} cos (1 - \frac{1}{4} x^{3}) d x

Apply u-substitution

= \int - \frac{4 cos ( u )}{3} d u

Take the constant out:

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

= - \frac{4}{3} \cdot \int cos (u) d u

Use the common integral:

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

= - \frac{4}{3} sin (u)

Substitute back

u = 1 - \frac{1}{4} x^{3}

= - \frac{4}{3} sin (1 - \frac{1}{4} x^{3})

Add a constant to the solution

= - \frac{4}{3} sin (1 - \frac{1}{4} x^{3}) + C

What is the integral of x^2cos(1-1/4 x^3) ?
The integral of x^2cos(1-1/4 x^3) is -4/3 sin(1-1/4 x^3)+C