Find the Antiderivative of f(x)= 3x^4 - square root of 8 x^8 + 5/9x^5

The antiderivative of the given function is the indefinite
integral of f(x).

We'll calculate the antiderivative of the function
you've provided:

f(x) = 3x^4dx - sqrt8*x^8 +
5/9x^5

We'll use the property of integral to be
additive:

Int f(x)dx = Int 3x^4dx - Int sqrt8*x^8 + (5/9)*Int x^-5
dx

Int f(x)dx = 3x^5/5 - 2sqrt2*x^9/9 + (5/9)*x^-4/-4 +
C

The anitderivative is 3x^5/5 - 2sqrt2*x^9/9 +
(5/9)*x^-4/-4 + C.