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Plz solve this integration.............. ∫ ((√((x)^2+x+1))/(x+1)) dx

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


     ∫ ((√((x)^2+x+1))/(x+1)) dx

Grade:11

4 Answers

Ramesh V
70 Points
12 years ago

∫ ((√((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

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

sry thats,

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

where x+1 is replaced by t

now it shld be clear for u

 

Moni RS
18 Points
12 years ago
Sir then the second step; is; ? ((v((t)^2-(t-1)))/t) dt right; then how to proceed sir.....

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