InterviewSolution
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InterviewSolution
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The integral `int(dx)/((sqrtx+root3(x^(2))))` represents the functionA. `6{root3(x^(2))-root3(x)+ln|1+root3(x)|}+C`B. `3root3(x^(2))-6root6(x)+6ln|1+root6(x)|+C`C. `3root3(x^(2))+6root6(x)+6ln|1+root6(x)|+C`D. `6root3(x^(2))-3root3(x)+6ln|1+root3(x)|+C` |
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Answer» Correct Answer - B Let `l=int(dx)/((sqrtx+root3(x^(2))))` `"Put "x=t^(6)` `therefore" "dx=6t^(5)dt` `"Then, "l=int(6t^(5)dt)/((t^(3)+t^(4)))=6int(t^(2)dr)/((1+t))` `=6int(t-1+(1)/(1+t))dt` `=6{(t^(2))/(2)-t+ln|1+t|}+C` `=3t^(2)-6t+6ln|1+t|+C` `=3t^(2)-6t+6ln|1+t|+C` `=3.root3(x)-6.root6(x)+6ln|1+root6(x)|+C` |
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