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Popular >

integral of 1/(x^3)csc(1/(x^2))cot(1/(x^2))

Solution

\int \frac{1}{x ^{3}} csc (\frac{1}{x ^{2}}) cot (\frac{1}{x ^{2}}) d x

Solution

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

Solution steps

\int \frac{1}{x ^{3}} csc (\frac{1}{x ^{2}}) cot (\frac{1}{x ^{2}}) d x

Apply u-substitution

: \int \frac{1}{2} d u

= \int \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2} u

Substitute back

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

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