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

The integral of xcsc(x^2)cot(x^2) is -1/2 csc(x^2)+C

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integral of xcsc(x^2)cot(x^2)

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

- \frac{1}{2} csc (x^{2}) + C

Solution steps

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

Apply u-substitution

: \int \frac{csc ( u ) cot ( u )}{2} d u

= \int \frac{csc ( u ) cot ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int csc (u) cot (u) d u

Apply u-substitution

: \int - 1 d v

= \frac{1}{2} \cdot \int - 1 d v

Integral of a constant:

\int a d x = a x

= \frac{1}{2} (- 1) v

Substitute back

= \frac{1}{2} (- 1) csc (x^{2})

Simplify

= - \frac{1}{2} csc (x^{2})

Add a constant to the solution

= - \frac{1}{2} csc (x^{2}) + C

\int \frac{1}{( x ^{2} + 25 )} d x

y = \frac{5}{7} x + \frac{4}{3}

y^{^{''}} + 2 y = 3, y (0) = - 1, y^{^{'}} (0) = 2

\frac{d}{d x} (lo g_{5} (2 x^{3} + x^{2}))

\int \frac{13}{r ^{2} + 1} d r

What is the integral of xcsc(x^2)cot(x^2) ?
The integral of xcsc(x^2)cot(x^2) is -1/2 csc(x^2)+C