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integration of sqrt(x/x+c)

integration of sqrt(x/x+c)

Grade:Upto college level

3 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

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..

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

Anjani Sai Kumar Chatla
31 Points
11 years ago

i found it difficult to type so, i have written it and scanned it.

vikas askiitian expert
509 Points
11 years ago

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

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