(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have various integration questions to do, and I do not want answers at all, just pointers on where to start.. I have 6 ones, and have only got anywhere with 2 of them (nt the two below)

Find integral of with respect to x:

1.

((x-1)/(x+1))^{1/2}* 1/x

2.

1/(2 - sin^{2}x)(2 + sinx - sin^{2}x)

2. Relevant equations

integration by substitution?

3. The attempt at a solution

For the first I tried u = x +1 but this doesn't go anywhere- I wouldn't know how to integrate it even without the extra 1/x term so really don't know where to start.

For the second I tried the substitution u = sin x thinking maybe this would lead to something where I could use partial fractions (it doesn't), and then there's no cos x to even allow the substitution in the first place.

My integration is REALLY rusty, so although I can manage integration by parts and simpler stuff, I seem to have completely lost the technique of what to substitute where.

One of the other ones is to find the integral of x * arcsin x dx. For this I get:

1/2(x^{2}* arcsinx + x (1-x^{2})^{1/2}- arcsin x ) + C

I can't find a problem in the working (I used integration by parts where u = x, u' = 1, v' = arcsin x, v = x * arcsin x + (1-x^{2})^{1/2}), but the maths program I use occasionally to check things came up with different coefficients in the answer.

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# Homework Help: Integration help needed!

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