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int(dx)/(x^(2)sqrt(x^(2)+a^(2)))...

int(dx)/(x^(2)sqrt(x^(2)+a^(2)))

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The integral int(x dx)/(2-x^(2)+sqrt(2-x^(2))) equals:

int_( then )(x-1)(dx)/(x^(2)(sqrt(2x^(2)-2x+1)))=(sqrt(f(x)))/(g(x))+c