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

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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.....