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Popular >

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

Solution

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

Solution

cot (\frac{1}{x}) + C

Solution steps

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

Apply u-substitution

: \int - csc^{2} (u) d u

= \int - csc^{2} (u) d u

Take the constant out:

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

= - \int csc^{2} (u) d u

Use the common integral:

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

= - (- cot (u))

Substitute back

u = \frac{1}{x}

= - (- cot (\frac{1}{x}))

Simplify

= cot (\frac{1}{x})

Add a constant to the solution

= cot (\frac{1}{x}) + C

Popular Examples

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\int (cos (x) + x) d x

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\int \frac{1 + x ^{2}}{x ^{4}} d x

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\int cos^{3} (7 x) sin (7 x) d x

integral of (x^3)/(x^4sqrt(16-x^2))

\int \frac{x ^{3}}{x ^{4} 16 - x ^{2}} d x

integral of sqrt((4x^2-12x+9)^3)

\int (4 x^{2} - 12 x + 9)^{3} d x

Frequently Asked Questions (FAQ)

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