What is the integral of x^2cos((x^3)/5) ?

The integral of x^2cos((x^3)/5) is 5/3 sin((x^3)/5)+C

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integral of x^2cos((x^3)/5)

\int x^{2} cos (\frac{x ^{3}}{5}) d x

\frac{5}{3} sin (\frac{x ^{3}}{5}) + C

Solution steps

\int x^{2} cos (\frac{x ^{3}}{5}) d x

Apply u-substitution

: \int \frac{u cos ( \frac{u ^{\frac{3}{2}}}{5} )}{2 x} d u

= \int \frac{cos ( \frac{u}{5} )}{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 (\frac{u}{5}) d u

Apply u-substitution

: \int cos (v) \cdot 5 d v

= \frac{1}{3} \cdot \int cos (v) \cdot 5 d v

Take the constant out:

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

= \frac{1}{3} \cdot 5 \cdot \int cos (v) d v

Use the common integral:

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

= \frac{1}{3} \cdot 5 sin (v)

Substitute back

= \frac{1}{3} \cdot 5 sin (\frac{x ^{3}}{5})

Simplify

\frac{1}{3} \cdot 5 sin (\frac{x ^{3}}{5}) : \frac{5}{3} sin (\frac{x ^{3}}{5})

= \frac{5}{3} sin (\frac{x ^{3}}{5})

Add a constant to the solution

= \frac{5}{3} sin (\frac{x ^{3}}{5}) + C

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

\frac{x}{x ^{2} + 1}

\int (5 + cot^{2} (x)) d x

\frac{s}{s ^{2} + 2 s}

x \to \infty lim (5 + \frac{3}{x})

What is the integral of x^2cos((x^3)/5) ?
The integral of x^2cos((x^3)/5) is 5/3 sin((x^3)/5)+C