please help me to solve this integration

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Roshdy

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∫1/ ( (x²+a²) √(x²+b²) ) dx

(x²+a²) myliplied by the root of (x²+b²) in the denominator
a & b are two different constants.
 

ArcTan[(Sqrt[ b^2-a^2] x)/(a Sqrt[b^2 + x^2])]/(a Sqrt[ b^2-a^2])

For a more general formula see Gradshteyn & Ryzhik 2.283 and 2.284
Hint: Try x/Sqrt[x^2+b^2]=t
 

    Roshdy

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Sure, but using pencil and paper is more funny. BTW, I'm a Math user since 1992 :wink:
 

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