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sadde prashanthi Grade: Upto college level
        integration of (x+1)/sqrt(x^2-x+1)
6 years ago

Answers : (2)

Sukhendra Reddy Rompally B.Tech Mining Machinery Engg, ISM Dhanbad
93 Points
										Dear student,
write the numerator as (2x-1)+3,then you can divide the integrand into 2 parts,1st one is a simple 1/root x form nd the second-write the denominator as root of (x-1/2)^2 + 3/4.i guess you can solve it from here.if you still have a problem,feel free to call me on 07209736303
6 years ago
vikas askiitian expert
510 Points
										

(x^2-x+1)=x^2-x+1/4+3/4


            =(x-1/2)^2 + 3/4


 integral(x+1)/sqrt(x^2-x+1)=x+1/sqrt{(x-1/2)^2 + 3/4}


 now put x-1/2=t


             dx=dt


 integral(t+3/2)/sqrt(t^2+3/4)


       = int{ t/sqrt(t^2+3/4)  + 3/4sqrt(t^2+3/4) }


       = sqrt(t^2 +3/4)   + 3/4log{sqrt(t^2+3/4) +t} +c


        =sqrt{ (x-1/2)^2 +3/4}   +   3/4 log{sqrt(x-1/2)^2 +x +1/4 } +c

6 years ago
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