- #1

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I'm struggling to figure out how to do integration with forms such as:

∫ x/(x+1) dx

∫ x/(x+1)^2 dx

∫(b-x)^2/(b-a) dx

This last one especially is giving me a strange issue, where if I plug it into wolfram:

https://www.wolframalpha.com/input/?i=integrate+(b+-+x)^2+/(b-a)++dx

It shows up with a result of (b-x)^3/3(b-a) + C

While if we know a to be a constant 0, and is left out, and this integral is plugged in: ∫(b-x)^2/(b) dx

https://www.wolframalpha.com/input/?i=integrate+(b+-+x)^2+/(b)++dx

The answer x^3/3b +bx -x^2 +C is produced

You get a different result than the result of the former with a =0. The former one ends up with a b^2 term in the end (if you expand the (b-x)^3 and divide by b), while the latter doesn't. What is happening here and how are these types of integrals solved?