Integration help needed!

  • Thread starter Zoe-b
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  • #1
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Homework Statement


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 - sin2x)(2 + sinx - sin2x)


Homework Equations


integration by substitution?


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(x2 * arcsinx + x (1-x2)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-x2)1/2), but the maths program I use occasionally to check things came up with different coefficients in the answer.
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
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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.

Try the substitution [itex]u=\sqrt{x+1}[/itex] instead and show your work.

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.

It's not clear exactly what the 2nd one is supposed to be....do you mean [tex]\int\frac{2+\sin x-\sin^2x}{2-\sin^2 x}dx[/tex] or [tex]\int\frac{dx}{(2-\sin^2 x)(2+\sin x-\sin^2 x)}[/tex] ?

In any case, there is a well-known trig identity that relates [itex]\cos x[/itex] to [itex]\sin x[/itex], so there is nothing to stop you from making your substitution.

One of the other ones is to find the integral of x * arcsin x dx. For this I get:
1/2(x2 * arcsinx + x (1-x2)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-x2)1/2), but the maths program I use occasionally to check things came up with different coefficients in the answer.

Post your workings then, because your final result is incorrect.
 
Last edited:
  • #3
hunt_mat
Homework Helper
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I think that for the trigonometric integral, you can use partial fractions.
 

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