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

The integral of x^2cot(x^3) is 1/3 ln|sin(x^3)|+C

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integral of x^2cot(x^3)

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

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

Solution steps

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

Apply u-substitution

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

= \int \frac{cot ( 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 cot (u) d u

Rewrite using trig identities

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

Apply u-substitution

: \int \frac{1}{v} d v

= \frac{1}{3} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{3} ln ∣ v ∣

Substitute back

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (\frac{3 x}{4 y})

3 x + \frac{5}{x}

\frac{d}{d x} (2^{t a n (4 x)})

\frac{d y}{d x} = y^{2} - 4

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

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