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

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

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

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

- sin (x^{3}) + C

Solution steps

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

Apply u-substitution

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

= - 3 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = x^{3}

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

Simplify

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

= - sin (x^{3})

Add a constant to the solution

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

\int_{8}^{16} 256 - x^{2} d x

\int_{- π}^{π} sin (2 x) d x

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

\frac{\partial}{\partial x} (\frac{2 x y}{x - y})

f (x) = \frac{x}{7}

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