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`        integration of sqrt(x/x+c)`
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
Let x=t^2
then i becomes t/sqrt(t^2+c) * 2t dt
ie 2t^2/sqrt(t^+c)
This can be easily integrated..

All the best.
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Sagar Singh
B.Tech, IIT Delhi

```
7 years ago
Anjani Sai Kumar Chatla
31 Points
```										i found it difficult to type so, i have written it and scanned it.
```
7 years ago
510 Points
```										f(x)=sqrt(x/x+c)
multiply and divide by x
I= int x/sqrt(x^2 +cx)
=int x/sqrt{(x+c/2)^2 -(c/2)^2}
put x+c/2 =t
dx=dt
I=int (t-c/2)/sqrt{ t^2-(c/2)^2 }
=int[  t/sqrt{t^2-(c/2)^2 }  - c/2sqrt{t^2- (c/2)^2} ]
=sqrt{t^2 - (c/2)^2 }   -c/2 . log[sqrt{t^2- (c/2)^2 + t} + k
=sqrt{ x^2 + cx}    -c/2 . log{sqrt(x^2+cx) + x +c/2 } + k
```
7 years ago
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