Integration Q (1 Viewer)

[shaon0]

Integrate: I=(1/(x+sqrt(x))

So far my working has been:
Let x= (cos@)^2
Also; x=0.5 [cos2@+1]
Thus, dx= -0.25sin2@ d@

I= S (1/(x+sqrt(x)) dx
= -0.25 S (2sin@cos@/(cos@[cos@+1]) d@
= -0.5 S [sin@/cos@+1] d@
= 0.5 ln(cos@+1)+C
= 0.5 ln[sqrt(x)+1] +C

But answer is 2ln[sqrt(x)+1) +C
I can't find my mistake, any help will be appreciated.

 

[azureus88]

Integrate: I=(1/(x+sqrt(x))

So far my working has been:
Let x= (cos@)^2
Also; x=0.5 [cos2@+1]
Thus, dx= -0.25sin2@ d@

I= S (1/(x+sqrt(x)) dx
= -0.25 S (2sin@cos@/(cos@[cos@+1]) d@
= -0.5 S [sin@/cos@+1] d@
= 0.5 ln(cos@+1)+C
= 0.5 ln[sqrt(x)+1] +C

But answer is 2ln[sqrt(x)+1) +C
I can't find my mistake, any help will be appreciated.

lol, its meant to be dx=-sin2@d@.

 

[shaon0]

lol, its meant to be dx=-sin2@d@.

lol. thanks for that.