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Integrate: x^-2/3 (1+x^2/3)^-1

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Solution: If we substitude  x=t^3    (as we know p belong to negative integer)

                   Let x=t^k ,where k is the LCM of m and n.

                    x=t^3Rightarrow dx=3t^2hspace0.1cmdt

               \Rightarrow I=int 3t^2/t^2 (1+t^2)hspace0.1cmdt\ \Rightarrow I=3int dt/t^2+1=3 an^-1(t)+c\ \Rightarrow I=3 an^-1(x^1/3)+c

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Deependra Verma

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