How do you integrate 1/(y(1-y))? Calculus Techniques of Integration Integral by Partial Fractions 2 Answers GiĆ³ May 18, 2015 Have a look: Answer link Antoine May 18, 2015 int1/(y(1-y))dy=-int1/(y^2-y+(-1/2)^2-(-1/2)^2)dy =>-int1/((y-1/2)^2-(1/2)^2)dy=-1/(1/2)^2int1/(((y-1/2)/(1/2))^2-1)dy=-4int1/((2y-1)^2-1)dy =>1/2*-4artanh(2y-1) + C = -ln|(1-2y+1)/(1+2y-1)| + C=ln|(y)/(1-y)| + C Answer link Related questions How do I find the partial fraction decomposition of (2x)/((x+3)(3x+1)) ? How do I find the partial fraction decomposition of (1)/(x^3+2x^2+x ? How do I find the partial fraction decomposition of (x^4+1)/(x^5+4x^3) ? How do I find the partial fraction decomposition of (x^4)/(x^4-1) ? How do I find the partial fraction decomposition of (t^4+t^2+1)/((t^2+1)(t^2+4)^2) ? How do I find the integral intt^2/(t+4)dt ? How do I find the integral int(x-9)/((x+5)(x-2))dx ? How do I find the integral int1/((w-4)(w+1))dw ? How do I find the integral intdx/(x^2(x-1)^2) ? How do I find the integral int(x^3+4)/(x^2+4)dx ? See all questions in Integral by Partial Fractions Impact of this question 29630 views around the world You can reuse this answer Creative Commons License