Hi all im trying to get my head around intergration by substitution and this one problem in particular has been giving me a problems any help?
substitute x = sine z into [int(x+x^2)/(1-x^2)^1/2 dx]
Easy.
You're trying to solve by substituting .
Notice that if you try to do this, you need to change the integral so it is with respect to instead of .
To do this, if then .
Thus .
Now substitute this all into the original integral, so that it becomes
.
Now use the fact that to get the answer back into terms of .
If then .
Also
.
Finally,
.
So this means that your answer is
.