Determine the integral: ∫dx/(x(x+2)^2 )?

Question

Please show steps. Thank you!

Answer 1

Given ʃdx/(x(x+2)^2)

Let

Substitute x=0, we get

                                 4A = 1 => A = 1/4

Taking coefficients of x^2 terms => A + B = 0

                                                         => B = -1/4

Taking coefficients of x terms => 4A + 2B + C = 0

                                                      => 4(1/4) + 2(-1/4) + C = 0

                                                      => 1 -1/2 + C = 0

                                                      => C = -1/2

Therefore

                          

                          

                           

 

 

Answer 2

step by step answer is