How do you integrate #int (3x)/sqrt((1-x^2))dx# using trigonometric substitution?

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Answer 1 · 2016-01-24T06:28:39

You need to use the beautiful Pythagorean right triangle.

Here is the general antiderivative :
#-3*sqrt(1- x^2)#

Here's a quick paint job to show you the lovely right triangle:

enter image source here

You now need to find the following:

#1)x#

#2)dx/(d theta)#

#3)sqrt(1-x^2)#

I'll give you a gentle and loving push in the right direction:

What is x?

Well, it sure looks to be :

#x = sin (theta)#

Your turn!