# Integration problem

## Homework Statement

I'm trying to do this problem from S. P. Thomson's Calculus Made Easy
(see attached image file)

## The Attempt at a Solution

I've produce the answer here, but it seems to be different from the mathcad solution, which is:
ln(-1+x)+ln(1+x)-ln(1+x^2)

Could someone help me see if (and if so, how) my answer is equivalent (without the constant). If it's wrong, I'd appreciate a pointer as to why, and if there is a quicker way of tackling this problem than by using partial fractions, could you let me know?

#### Attachments

• ex 004.jpg
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Your answer is correct as is the books. ln a + ln b = ln (ab).

HallsofIvy
$$ln\left(\frac{x^2-1}{x^2+1}\right)+ C$$
$$ln\left(C'\frac{x^2-1}{x^2+1}\right)$$