Trigonometric Substitution Problem - Calculus 2

khatche4
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Hey there
This is a trig substitution for my Calculus 2 class and I really have NO idea how to get started...

\int\frac{4}{\sqrt{3-2x^2}}dx

My professor has yet to go over how to evaluate trigonometric substitutions with coefficients in front of variables.
 
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how about factoring out the 2?
 
How would you factor out the two?

Because \sqrt{3-2x^2} is not the same as 2*\sqrt{\frac{3}{2}-x^2}
 
khatche4 said:
How would you factor out the two?

Because \sqrt{3-2x^2} is not the same as 2*\sqrt{\frac{3}{2}-x^2}

Yes, but \sqrt{3-2x^2} = \sqrt{2}*\sqrt{\frac{3}{2}-x^2}. I may not have been clear in my previous post.
 
Oh! Duh! Thank you!
I'll give it a try.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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