Find the particular antiderivative that satisfies the following conditions:
F′(x)=x^3+5sqrtx ;F(1)=−9
F′(x)=x^3+5sqrtx
= x^3 + 5x^(1/2)
F(x) = (1/4)x^4 + (2/3)(5)x^(3/2) + c
= (1/4)x^4 + (10/3)x^(3/2) + c
given F(1) = 9
(1/4)(1) + (10/3)(1) + c = 9
c = 9 - 1/4 - 10/3
= ((108/12 - 3/12 - 40/12) = 65/12
F(x) = (1/4) x^4 + (10/3) x^(3/2) + 65/12