The integral `int(dx)/((sqrtx+root3(x^(2))))` represents the function

Options

A. `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`

Answer

B

Explanation

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`