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integral of dx/(x^2+1)x^0.5

integral of dx/(x^2+1)x^0.5

Grade:12

5 Answers

souvik das
33 Points
11 years ago

proceed this way

 

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Anil Pannikar AskiitiansExpert-IITB
85 Points
11 years ago

Dear Shivan,

 put x = t2

dx = 2tdt

so intergral is -   2dt/(t4+1)

 =  2 [ (t2+1) - (t2-1) ] /(t4+1)  dt

solve intergral (t2+1)/(t4+1) = (1+ 1/t2)/[(t-1/t)2 + 2]

now pur t-1/t = y or (1+ 1/t2)dt = dy

put above value in integral and solve

similarly, solve intergral : (t2-1)/(t4+1)

 

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Anil Pannikar

IIT Bombay

 

Surya Anuraag Duvvuri
39 Points
11 years ago

    Hello,

            Iam Surya Anuraag.Here is your answer,

            dx/(x^2+1)x^0.5 ,

            put x^0.5 = t , dx/2(x)^0.5=dt, => dx/x^0.5=2dt

             now  it wll be in the form,

              2dt/(t^4+1)=(t^2+1)dt/(t^4+1) - (t^2-1)dt/(t^4+1)

              now you can simplify quite easily by takung x^2 common from both nm.,&dm.,   from two fractions and by putting the integrals of the nm`s.,as a function

                                                                         Thankyou.

pranay -askiitians expert
44 Points
11 years ago

is it 4/3 log x

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago

Thanks and Regards 
Sher Mohammad
Askiitians Faculty,
B.tech, IIT Delhi

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