Mastering Double Integrals: Solving Tricky Problems with 1/(1-xy) Function

[cragar]

Homework Statement

integral of 1/(1-xy)dxdy x's from 0 to 1 and y's from 0 to 1

The Attempt at a Solution

ok so the first integral gives -ln|1-y|/(y) after we evaluated the x's from 0 to 1
but I am having trouble with integrating with respect to y .

 

[Mark44]

Did you use integration by parts for the integrand above? If so, are you getting something like
$$\int \frac{dy}{y^2(1 - y)}$$

For an integrand like that you want to rewrite the expression as A/y + B/y² + C/(1 - y). To do this, set 1/(y²(1 - y)) equal to A/y + B/y² + C/(1 - y) and solve for A, B, and C. This equation has to be identically true for all y.

BTW, since y ranges from 0 to 1, 1 - y is always nonnegative, so you don't need the absolute values around it.

 

[cragar]

ok thanks