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

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
--
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
```
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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