find the most general antiderivative of

Question

Find the most general antiderivative of f(x)=−2−2x3−8x5−6x7.

Answer 1

Answer 2

f(x)=−2−2x3−8x5−6x7.

f(x) = 2-2x³ - 8x⁵ - 6x⁷

f'(x) = 0 -2(3)x² -8(5)x⁴ - 6(7)x⁶

f'(x) = -6x² - 40x⁴ - 42x⁶

Answer 3

I'm going to assume that the number after each "x" is an exponent. Going off that assumption, there is a common formula for the antiderivative (also called an integral) of xⁿ, that being xⁿ⁺¹/(n+1).

Your function can be rewritten as f(x)=-2x⁰-2x³-8x⁵-6x⁷. This integrates to -(2/1)x¹-(2/4)x⁴-(8/6)x⁶-(6/8)x⁸ which simplifies to -2x-(1/2)x⁴-(4/3)x⁶-(3/4)x⁸.