What is the integral of 1/((1-xy)^2) ?

The integral of 1/((1-xy)^2) is 1/(y(1-yx))+C

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integral of 1/((1-xy)^2)

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

\frac{1}{y ( 1 - y x )} + C

Solution steps

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

Apply u-substitution

= \int - \frac{1}{y u ^{2}} d u

Take the constant out:

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

= - \frac{1}{y} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= - \frac{1}{y} (- \frac{1}{u})

Substitute back

u = 1 - y x

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

Simplify

- \frac{1}{y} (- \frac{1}{1 - y x}) : \frac{1}{y ( 1 - y x )}

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

Add a constant to the solution

= \frac{1}{y ( 1 - y x )} + C

What is the integral of 1/((1-xy)^2) ?
The integral of 1/((1-xy)^2) is 1/(y(1-yx))+C