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]

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- Dec 8th 2009, 10:03 PMGeordie-boyintergration by substitution
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] - Dec 8th 2009, 10:15 PM11rdc11
- Dec 8th 2009, 10:27 PMProve It
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

. - Dec 8th 2009, 10:27 PMCalculus26
See attachment