Question

`int (4x)/(1-x^4)dx` =?

Answer 1

Notice that

`4(x/(1-x^4))=2x/( (x^2+1))-1/( (x-1))-1/( (x+1))`

Hence

#int x/(1-x^4)dx=2int x/( (x^2+1))dx-int1/( (x-1))dx-int1/( (x+1))dx=log(x^2+1)-log(x-1)-log(x+1)+c= log(x^2+1)-log(x^2-1)+c#