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

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

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integral of (1-xy)^{-2}

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

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

Solution steps

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

Apply u-substitution

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

= \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}{u}

= - \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

\int 4 tan^{3} (2 x) sec^{5} (2 x) d x

\int (e^{- 3 x}) d x

\frac{d y}{y} = \frac{4}{x} d x

f (x) = sec (2 x)

x \to 3 lim (\frac{x ^{3} - 8}{x - 2})

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