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

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

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integral of x^2cos(x^3)

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

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

Solution steps

\int x^{2} cos (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 = x^{3}

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

Add a constant to the solution

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

x \to 1 lim (- x^{2} + 9 x - 7)

(1 + e^{x}) \frac{d y}{d x} + e^{x} y = 0

\int \frac{3 x}{x + 2} d x

y^{^{'}} = 0.05 y + 5500

x \to 0 lim (1 - \frac{cos ( 3 x )}{x})

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