InterviewSolution
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InterviewSolution
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`(1)/(x^((1)/(2))+x^((1)/(3)))` संकेत `(1)/(x^((1)/(2))+x^((1)/(3)))=(1)/(x^((1)/(3))(1+x^((1)/(6)))), x=t^(6)` रखिए । |
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Answer» माना `I=int(1)/(x^(1//2)+x^(1//3))dx` माना `x=t^(6)" "rArr" "dx=6t^(5)dt` `therefore" "I=int(6t^(5))/((t^(6))^(1//2)+(t^(6))^(1//3))dt=6int(t^(5))/(t^(3)+t^(2))dt` `" "=6int(t^(5))/(t^(2)(t+1))dt=6int(t^(3))/((t+1))dt` `" "=6int((t^(3)+1-1)/(t+1))dt` `" "=6int[((t+1)(t^(2)-t+1))/(t+1)-(1)/(t+1)]dt` `" "=6int(t^(2)-t+1-(1)/(t+1))dt` `" "=6((t^(3))/(3)-(t^(2))/(2)+t-log|t+1|)+C` `" "=6{((x^(1//6))^(3))/(3)-((x^(1//6))^(2))/(2)+(x^(1//6))-log|x^(1//6)+1|+C}` `" "(because t=x^(1//6))` `" "=2x^(1//2)-3x^(1//3)+6x^(1//6)-6log|x^(1//6)+1|+c` |
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