InterviewSolution
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InterviewSolution
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Evaluate: `int1/(x^(1//2)+x^(1//3)) dx` |
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Answer» `(1)/(x^(1//2)+x^(1//3))=(1)/(x^(1//3)(1+x^(1//6)))` Let `x=t^(6)impliesdx=6t^(5) dt` ` :. int(1)/(x^(1//2)+x^(1//3))dx=int(1)/(x^(1//3)(1+x^(1//6)))dx` `=int(6t^(5))/(t^(2)(1+t))dt` `=6int(t^(3))/((1+t))dt` On dividing, we obtain `int(1)/(x^(1//2)+x^(1//3))dx=6int{(t^(2)-t+1)-(1)/(1+t)}dt` `=6[((t^(3))/(3))-((t^(2))/(3))+t-log|1+t|]+C` `=2x^(1//2)-3x^(1//3)+6x^(1//6)-6 log(1+x^(1//6))+C` |
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