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Evaluate: int (dx)/(x^(1/2)+x^(1/3))...

Evaluate: `int (dx)/(x^(1/2)+x^(1/3))`

Text Solution

Verified by Experts

The correct Answer is:
`2sqrt(x)-3x^(1//3)+6x^(1//6)-6log|1+x^(1//6)|+C`
`I=int(dx)/(x^(1//3)(1+x^(1//6)))*"Now Put "x=t^(6)anddx=6t^(5)dt`.
Then, =`I=6int(t^(3))/(1+t)dt=6*int(t^(2)-t+1-(1)/(1+t))dt`.
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