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Moni RS Grade: 11
        

Plz solve this integration..............


     ∫ ((√((x)^2+x+1))/(x+1)) dx

8 years ago

Answers : (4)

Ramesh V
70 Points
										

∫ ((√((x)2+x+1))/(x+1)) dx


put x+1 = t   , dx=dt


∫ ((√((t)2-(t-1)2))/t) dt


∫ ((√(2t-1)))/2.t) dt


put  2t-1 = m2   , dt =2m.dm


2.∫m2 /(1+m2)dm


2.∫dm  - 2.∫1 /(1+m2)dm 


2m - tan-1m +C


2.√(2x+1) -  2.tan-1√(2x+1) +C


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Regards,
Ramesh  
IIT Kgp - 05 batch

8 years ago
Moni RS
18 Points
										Sir, i didn't understand the second step, can u plz explain it sir.............
										
8 years ago
Ramesh V
70 Points
										

sry thats,


x2+x+1 = (x+1)2 - x


where x+1 is replaced by t


now it shld be clear for u


 

8 years ago
Moni RS
18 Points
										Sir then the second step;


is;
? ((v((t)^2-(t-1)))/t) dt
right; then how to proceed sir.....
8 years ago
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