- #1
Xilor
- 152
- 7
Hi,
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?
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?