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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 3 \cdot \int x^{2} sin (x^{3} - 1) d x

Apply u-substitution

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

= 3 \cdot \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

= 3 \cdot \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

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

Substitute back

u = x^{3} - 1

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

Simplify

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

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

Add a constant to the solution

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

- 4 t (3 t^{5} - 1)^{4}

\frac{d}{d x} (ln (x x^{2} - 10))

f (x) = 4 x^{2} - 3 x + 2

\int_{0}^{5} x^{2} d x

\frac{d}{d x} (y^{1 - n})

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