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

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

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

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

- cot (ln (x)) + C

Solution steps

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

\int e^{2 x} e^{x} d x

\int \frac{3 x + 8}{9 x ^{2} - 3 x - 1} d x

\int (x + 1)^{9} d x

\int x^{2} 1 + 2 x^{3} d x

\int \frac{3}{4 x ^{3}} d x

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