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

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

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integral of sin(x^3)x^2

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

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

Solution steps

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

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 = x^{3}

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

Simplify

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

Add a constant to the solution

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

\int \frac{1 - x}{x ^{2}} d x

x \to 0 - lim (\frac{x - 1}{x ^{2}})

f (t) = sin (t^{2})

\frac{d y}{d x} + (\frac{7}{x}) y = 2 x + 3

\frac{d}{d x} ((3 x^{2})^{2 x} (x^{2} + 2 x)^{2})

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