What is the integral of x/(x^2sin^2(ln(x))) ?

The integral of x/(x^2sin^2(ln(x))) is -cot(ln(x))+C

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integral of x/(x^2sin^2(ln(x)))

\int \frac{x}{x ^{2} sin ^{2} ( ln ( x ) )} d x

- cot (ln (x)) + C

Solution steps

\int \frac{x}{x ^{2} sin ^{2} ( ln ( x ) )} d x

Cancel the common factor:

x

= \int \frac{1}{x sin ^{2} ( ln ( x ) )} d x

Apply u-substitution

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

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

Use the common integral:

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

= - cot (u)

Substitute back

u = ln (x)

= - cot (ln (x))

Add a constant to the solution

= - cot (ln (x)) + C

\frac{( x + 5 )}{( x - 5 )}

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\frac{\partial}{\partial y} (9 e^{yz} cos (x yz))

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