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

∫ ((√((x)^2+x+1))/(x+1)) dx

∫ ((√((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

--

Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult
to understand - post it here and we will get you the answer and detailed solution very quickly.We are all
IITians and here to help you in your IIT JEE preparation. All the best.

Regards,
Ramesh  
IIT Kgp - 05 batch

Sir, i didn't understand the second step, can u plz explain it sir.............

sry thats,

x²+x+1 = (x+1)² - x

where x+1 is replaced by t

now it shld be clear for u

 

Sir then the second step; is; ? ((v((t)^2-(t-1)))/t) dt right; then how to proceed sir.....