Question #800f5

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Answer 1 · 2017-06-04T09:25:31

#\int(x^(1/2)-x^(-1/2))^2"d"x = \int(x-2+x^-1)"d"x#
#\int(x^(1/2)-x^(-1/2))^2"d"x = x^2/2-2x+ln\abs(x)+C#

Answer 2 · 2017-06-04T10:45:19

#x^2/2-2x+lnx+C.#

Let, #I=int(sqrtx-1/sqrtx)^2dx.#

Knowing that, #(1) : inty^ndy=y^(n+1)/(n+1)+c, n!=-1, and,#

# (2) : int1/xdx=ln|x|+c', # we have,

#I=int(sqrtx-1/sqrtx)^2dx,#

#=int(x-2+1/x)dx,............[because," squaring]"#

#=intx^1dx-2intx^0dx+int1/xdx,#

#=x^(1+1)/2-2*x^(0+1)/(0+1)+ln|x|,#

# rArr I=x^2/2-2x+ln|x|+C.#

Enjoy Maths.!