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Evaluate:int(x+x^(2/3)+x^(1/6))/(x(1+x^(...

Evaluate:`int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3)))dx` equals

A

`(3x^((2)/(3)))/(4)+6tan^(-1)(x^((1)/(6)))+C`

B

`(3x^((2)/(3)))/(2)+6tan^(-1)(x^((1)/(6)))+C`

C

`(3x^((2)/(3)))/(10)+6tan^(-1)(x^((1)/(6)))+C`

D

`(3x^((2)/(3)))/(5)+6tan^(-1)(x^((1)/(6)))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x=u^(6)`
`therefore" "I=6int(u^(5)+u^(3)+1)/(1+u^(2))du`
`=6intu^(3)du+6int(du)/(1+u^(2))`
`=(3u^(4))/(2)+6 tan^(-1)u+C`
`=(3x^((2)/(3)))/(2)+6 tan^(-1)(x^((1)/(6)))+C`
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