How do you find the most general antiderivative or indefinite integral #int (1/7-1/y^(5/4)) dy#?

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Answer 1 · 2017-02-07T06:52:29

#1/7y-5/y^(1/4)+C.#

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

#(2): int[kf(y)-g(y)]dy=kintf(y)dy-intg(y)dy, k" is a const."#

#"Therefore, "int(1/7-1/y^(5/4))dy#

#=1/7inty^0dy-inty^(-5/4)dy#

#=1/7y^(0+1)/(0+1)-(-5/4)(y^(-5/4+1))/((-5/4+1))#

#=1/7y+{(5/4)/(-1/4)}y^(-1/4)#

#=1/7y-5/y^(1/4)+C.#