Antiderivative F that satisfies F(1)=0

Question

For the function​ f, given​ below, find the antiderivative F that satisfies ​F(1)=0.

​f(x)=x⁶−2x^-3+5

The antiderivative that satisfies the given condition is ​F(x)=___________

Answer 1

f(x) = x^6 -2x^-3 +5

integrate. Increase each exponent by one and divide by the same

6+1 = 7,

-3+1 = -2

0+1 = 1 (5 is the same as 5x^0, x^1 is the same as x)

then add an unknown constant C

F(x) = x^7/7 -2x^-2/-2 +5x + C

F(x) = (1/7)x^7 +1/x^2 +5x + C

plug in x=1 to solve for C

F(1) = 0 = 1/7 +1/2 +5 + C

C = -1/7-1/2 -5

C = -2/14 -7/14 -70/14

C = -79/14

C =-5 9/14

F(x) = (1/7)x^7 + 1/x^ 2+ 5x - 79/14