Evaluate the integral. ?

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Answer 1 · 2017-12-14T06:13:33

# 9/2+ln(3/2).#

Let, #I=int_2^3 (sqrtx+1/sqrtx)^2dx.#

Using, #(a+b)^2=a^2+2ab+b^2,# we have,

#(sqrtx+1/sqrtx)^2=(sqrtx)^2+2(sqrtx)(1/sqrtx)+(1/sqrtx)^2,#

#=x+2+1/x.#

#:. I=int_2^3(x+2+1/x)dx,#

#=[x^2/2+2x+ln|x|]_2^3,#

#=[9/2+2*3+ln|3|]-[4/2+2*2+ln|2|],#

#=9/2+(ln3-ln2),#

#rArr I=9/2+ln(3/2).#