Well, darling, the antiderivative of 70x is 35x^2 + C, where C is the constant of integration. It's as simple as that, honey. Just integrate like there's no tomorrow and don't forget that little "+ C" at the end.
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252-70x+49 = (5x-7)(5x-7) when factored
I assume you mean -10x^4? In that case, antiderivative would be to add one to the exponent, then divide by the exponent. So -10x^5, then divide by 5. So the antiderivative is -2x^5.
By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2
(that weird integral or antiderivative sign) x^(-6/5) dx =-5*x^(-1/5)
Yes.