Help finding integral of trigonometric function

student93
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Homework Statement



4∫tan(x^2)dx from 0 to √(π)/2

Homework Equations



4∫tan(x^2)dx from 0 to √(π)/2

The Attempt at a Solution



I tried doing u-substitution, which didn't work, and also tried to look for a trig identity and wasn't able to find any relevant one.
 
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Have you tried changing it to a ratio of sine and cosine and integrating by parts?
How about changing it to exponential form and tackling that?

in general trig functions of x^2 are pretty nasty.
If this is part of an exercise you should look to your notes about similar functions.
If not you may want to consider working your actual problem by another means.
 
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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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