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I=int(1)^(2)(dx)/(sqrt(2x^(3)-9x^(2)+12x...

I=int_(1)^(2)(dx)/(sqrt(2x^(3)-9x^(2)+12x+4))

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int(dx)/(sqrt(x^(2)-9)+sqrt(x^(2)-4))=

int(dx)/(sqrt(9x^(2)-4))

int(dx)/(sqrt(1-9x^(2)))

int(dx)/(sqrt(1-9x^(2)))

Let I_(1)=int_(1)^(2)(x)/(sqrt(1+x^(2)))dx and I_(2)=int_(1)^(2)(1)/(x)dx .Then

int (1)/((x^(2)+9)sqrt(x^(2)-9))dx=