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

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

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

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

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

Solution steps

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

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 = 1 - x^{3}

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

Add a constant to the solution

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

x \to 0 lim (\frac{3 ^{s i n (x)} - 1}{4 x})

25 y^{^{''}} + 10 y = 0

\frac{d}{d x} (- ln (4 x))

\int (- 8 sec (x) tan (x) - 3 sec^{2} (x)) d x

y^{^{''}} + 5 y^{^{'}} - 6 y = (3 x - 1) e^{x}

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