Originally Posted by roshanhero I am sorry but shouldnot there have been Yes. So the integral actually becomes .
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Originally Posted by Prove It The first two have been taken care of. for you do not use a substitution. You use a trigonometric substitution. . Now use the substitution . Note that . So . Therefore . Now remembering that . So finally our answer is . Actually I think doing a u-substitution for this problem would be much easier than doing a trig substitution. start by noticing that = let u = 2x and du = 2 dx. then you would get then you would get the same answer with much less work.
Originally Posted by oblixps Actually I think doing a u-substitution for this problem would be much easier than doing a trig substitution. start by noticing that = let u = 2x and du = 2 dx. then you would get then you would get the same answer with much less work. That's only if you remember the rule for , which was found from trigonometric substitution...
Originally Posted by Prove It That's only if you remember the rule for , which was found from trigonometric substitution... I only used the definition of the derivative of arctan(x) along with a simple u-substitution to find this integral. no need for trig sub.
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