Integration problem?

Question

How to integrate 1/((x)(x+1)^2)?I don't need the answer (it would be nice), just how to solve the problem.

Answer 1

take 1/2 as common outside the integral and use partial fraction formula to integrate the rest.
that should be : integral of 1/x +integral of 1/x+1
you will know to integrate this

Answer 2

oks here's what U have to do... :)

ever heard the term "partial fractions"......
try using that methos on this..

since u'd asked not to give the answer im not gonna write the answer. but will give u the first step...

1/[(x)(x+1)^2] = A/x + B/(x+1) + C/(x+1)^2

solve this (its too easy Im not gonna solve it here). then you'll get these..

A=1
B=C= -1

so

int (1/[(x)(x+1)^2]) == int( 1/x -1/(x+1) - 1/(x+1)^2)

now its pretty clear what the answer is..... lol.... :) :) :)
Good luck!!

Answer 3

1/(x(x+1)^2)=1/(x(x+1)(x+1)) now resolve this into partial fractions as A/x+B/(x+1)+C/(x+1)^2 and use standard integrals
since you did not want me to solve it fully i amstopping withthe hint.the answer will be like A log x+B log (x+1)-C/(x+1)+D