InterviewSolution
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InterviewSolution
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`int(x)/((x^(4)-x^(2)+1))dx` का मान ज्ञात कीजिए । |
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Answer» `int(x)/((x^(4)-x^(2)+1))dx` यदि `t=x^(2) rArr 2x dx = dt,` तब `int(x)/((x^(4)-x^(2)+1))dx=(1)/(2).int(dt)/((t^(2)-t+1))` `=(1)/(2).int(dt)/({(t-(1)/(2))^(2)+((sqrt3)/(2))^(2)})` `=(1)/(2).(1)/(((sqrt3)/(2)))tan^(-1).((t-(1)/(2)))/(((sqrt3)/(2)))+c` `=(1)/(sqrt3)tan^(-1)((2t-1)/(sqrt3))+c` `=(1)/(sqrt3)tan^(-1)((2x^(2)-1)/(sqrt3))+c` |
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