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" 10."int(1)^(2)(dx)/((x+1)sqrt(x^(2)-1)...

" 10."int_(1)^(2)(dx)/((x+1)sqrt(x^(2)-1))

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int_(1)^(2)(1)/(x sqrt(x^(2)-1))dx=

int_(-1)^(1)(dx)/((2-x)sqrt(1-x^(2)))

"int_(-1)^(1)(dx)/((2-x)sqrt(1-x^(2)))

int_(1)^(2)(dx)/((x+1)sqrt(x^(2)-1))=(1)/(sqrt(3))

int_(0)^(1/sqrt2)(dx)/(sqrt(1-x^(2)))

int_(1)^(2) (x)/(sqrt(1+2x^(2)))dx

int_(1)^(2) (x)/(sqrt(1+2x^(2)))dx

If I_(1) = int_(1)^(2)(dx)/(sqrt(1+x^(2))) and I_(2)= int_(1)^(2) (dx)/(x) then

int_(1//2)^(1)(1)/(sqrt(1-x^(2)))dx=

int(2x+1dx)/( sqrt(x^(2)+x+1))