InterviewSolution
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InterviewSolution
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`int(1)/(x(2+x^(5)))dx` का मान ज्ञात कीजिए । |
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Answer» `int(1)/(x(2+x^(5)))dx=int(x^(4))/(x^(5)(2+x^(5)))dx` माना `2+x^(5)=t rArr 5x^(4)dx=dt` `therefore" "int(1)/(x(2+x^(3)))dx=int(x^(4))/(x^(5)(2+x^(5)))dx` `=(1)/(5)int(dt)/((t-2)t)=(1)/(5)int[(1)/(2(t-2))-(1)/(2t)]dt` `=(1)/(10)[int(1)/((t-2))dt-int(1)/(t)dt]` `=(1)/(10)[log(t-2)-logt]=(1)/(10)log((t-2)/(t))+c` `=(1)/(10)log((2+x^(5)-2)/(2+x^(5)))+c` `=(1)/(10)log((x^(5))/(2+x^(5)))+c` |
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