The integral of dx/x^2 sqrt(x^2 + 9) from sqrt(3) to cube root of 3 Using trigonometric substitution

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Evaluate `int_(sqrt(3))^(root(3)(3))(dx)/(x^2sqrt(x^2+9))` :

Let `x=3tanu` . Then `dx=3sec^2udu` .

Now `sqrt(x^2+9)=sqrt(9tan^2u+9)=sqrt(9(tan^2u+1))=3secu` ; also `u=tan^(-1)(x/3)` .

So ignoring the...

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