Grade 12th passDifferential Calculus
what is the integration of the following statement∫sqrt(1+ 1/x) dx
what is the integration of the following statement
∫sqrt(1+ 1/x) dx
1 Answer
Aditya Gupta
let u=sqrt(1+ 1/x)
or u^2= (1+ 1/x)
2udu= – dx/x^2
so integral becomes udx= –u*2ux^2du= – 2(ux)^2du= – 2u^2(1/(u^2 – 1))^2du
now u^2(1/(u^2 – 1))^2= u^2/(u^2 – 1)^2= u^2/(u – 1)^2(u+1)^2, which can be easily solved using partial fractions.
u^2/(u – 1)^2(u+1)^2= A/(u-1)+B/(u-1)^2+C/(u+1)+D/(u+1)^2, now determine the coeffs A, B, C, D in the usual way and you are good to go!
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