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I need help with the following integral: I tried various types of substitutions of irrational functions, but nothing seems to simplify the integral. Note: I want to work in real domain, not in complex, so factoring the polynomial in the square root doesn’t help.

I need help with the following integral:
 
I tried various types of substitutions of irrational functions, but nothing seems to simplify the integral.
 
Note: I want to work in real domain, not in complex, so factoring the polynomial in the square root doesn’t help.

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