I am working on a problem which involves integrating [with limits 0, 1 (don't know how to do limits in latex)].
So I managed to integrate using substitution as follows:
let u = 1+x, du/dx = 1, limits: u = 1+1 = 2 and u = 1+0=1
x = u-1.
[with different limits 1, 2]
I expand out:
and I get a result of 5/6 - ln2.
I am then asked to integrate this: with limits 0 to 1.
So I start integrating (by parts) and notice that second integration bit - I have this:
That last bit, I already integrated above.
So my question is, how do I combine the two. My start part of integration by parts and then the minus - and here use my previous result.
The previous result had different limits - so I presume I cant just use the result. Do I just substitute back in 1+x for the u above like this:
- then use my limits 0, 1 as asked for this integration?