Is the solution for trig substitution correct?

[nameVoid]

Homework Statement

I(1/(9x^2+6x-8)^(1/2),x)
I( 1/( (3x+1)^2-9 )^(1/2),x )
3x+1=3secT
dx=secTtanTdT
I( (secTtanT)/3tanT,T )
(1/3)I( secT,T)
(1/3)|secT+tanT|+C
secT=(3x+1)/3
tanT=(9x^2+6x-8)^(1/2)/3
solution: (1/3)|(3x+1)/3+(9x^2+6x-8)^(1/2)/3|
my book is showing :(1/3)|(3x+1)+(9x^2+6x-8)^(1/2)|

Homework Equations

The Attempt at a Solution

 

[queenofbabes]

Homework Statement

I(1/(9x^2+6x-8)^(1/2),x)
I( 1/( (3x+1)^2-9 )^(1/2),x )
3x+1=3secT
dx=secTtanTdT
I( (secTtanT)/3tanT,T )
(1/3)I( secT,T)
(1/3)|secT+tanT|+C
secT=(3x+1)/3
tanT=(9x^2+6x-8)^(1/2)/3
solution: (1/3)|(3x+1)/3+(9x^2+6x-8)^(1/2)/3|
my book is showing :(1/3)|(3x+1)+(9x^2+6x-8)^(1/2)|

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