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sadde prashanthi Grade: Upto college level
        

integration of sqrt(x/x+c)

7 years ago

Answers : (3)

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..








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Askiitians Expert


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
vikas askiitian expert
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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