InterviewSolution
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InterviewSolution
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If `l=int(x^(5))/(sqrt(1+x^(3)))dx`, then l is equal toA. `(2)/(9)(1+x^(3))^((5)/(2))+(2)/(3)(1+x^(3))^((3)/(2))+C`B. `log|sqrtx+sqrt(1+x^(3))|+C`C. `log|sqrtx-sqrt(1+x^(3))|+C`D. `(2)/(9)(1+x^(3))^((3)/(2))-(2)/(3)(1+x^(3))^((1)/(2))+C` |
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Answer» Correct Answer - D Given, `" "l=int(x^(5))/(sqrt(1+x^(3)))dx` Let`" "1+x^(3)=t` `rArr" "3x^(2)dx=dt` `therefore" "l=int((t-1))/(sqrtt).(dt)/(3)=(1)/(3)int(sqrtt-t^(-1//2))dt` `=(1)/(3)[(2t^(3//2))/(3)-2t^(1//2)]+c` `=(2)/(9)(1+x^(3))^(3//2)-(2)/(3)(1+x^(3))^(1//2)+C` |
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