Your substitution and work is fine - when your answer is differentiated the integrand is obtained, you've included the arbitrary constant of integration, so all is well.

But remember that your answer includes an arbitrary constant (of integration) C ..... This is (probably) the clue that answers your question ......

Note that . When this is integrated, you get . This answer is also correct. Is it the book's answer? How can twoapparentlydifferent answers be explained?? Well ......

What happens if you replace the arbitrary constant C ofyouranswer with theequally arbitrary....?