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

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

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integral of x^2*sin(x^3)

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

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

Solution steps

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

n = 1 \sum \infty 15 (\frac{1}{100})^{n}

\frac{d}{d x} (\frac{x ^{2}}{2} + \frac{1}{x})

x (x^{5} + 2)

x \to 0 lim ((2 x^{2} + x)^{x})

y^{^{''}} + y = \frac{1}{( cos ( 2 x ) ) ^{\frac{3}{2}}}

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