How do you integrate #x^(-1/2) - sqrt(x) #?

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Answer 1 · 2018-02-07T18:02:32

# 2/3(3-x)x^(1/2)+C.#

We have, #intt^ndt=t^(n+1)/(n+1)+c, n ne -1#.

#:. int{x^(-1/2)-sqrtx}dx#,

#=int{x^(-1/2)-x^(1/2)}dx#,

#=intx^(-1/2)dx-intx^(1/2)dx#,

#=x^(-1/2+1)/(-1/2+1)-x^(1/2+1)/(1/2+1)#,

#=2x^(1/2)-2/3x^(3/2)#,

#=2/3(3-x)x^(1/2)+C.#