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int(sec^2x)/(sqrt(2tan^2x+3tanx+3))dx=...

`int(sec^2x)/(sqrt(2tan^2x+3tanx+3))dx=`

A

`log|tanx+(3)/(2)+sqrt(tan^2x+(3tanx)/(2)+(3)/(2))|+c`

B

`log|tanx+(1)/(2)+sqrt(tan^2x+(3tanx)/(2)+(3)/(2))|+c`

C

`(1)/(sqrt(2))log|tanx+(3)/(4)+sqrt(tan^2x+(3tanx)/(2)+(3)/(2))|+c`

D

`(1)/(sqrt(2))log|tanx+(1)/(4)+sqrt(tan^2x+(3tanx)/(2)+(3)/(2))|+c`

Text Solution

Verified by Experts

The correct Answer is:
C
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