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# Find the most general antiderivative of the function. (Check your answers by differentiation.)$f(x) = 7x^{2/5} + 8x^{-4/5}$

## $5 x^{7 / 5}+40 x^{1 / 5}+C$

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Okay, so we're being asked to find the most general anti druid of the function after back people seven Exeter plus eight X to the minus four shift. So if we're trying to take so essentially we're taking the integral of ethnic DX, and we're going to get some anti derivative effort back and so well, how you get FX will. First, we're gonna put this thing in the Angels of seven. Next to to the fifth plus eight eggs, your mind is forfeit. And remember that for expert and the anti driven who would just add on to the ex opponent and divide that, um, underneath the in Crete a fraction so it will be a little more clear. So, Toby seven x and you have to tell affair. And then what you're gonna do is you're going to say, plus one and all over two ships plus one as well, and it is coming for us, eh? Thanks to the mining forfeit. And there's also baby plus one over minus four fifths plus one. Okay, so when you do that, what you get where you get a good seven x to these seven fifth, so that's going to be over seventy fifth and plus, um, a ex, the one fifth over one fifth and then remembered at a constant. And then now, when you have a fraction of the numerator, you just take the reciprocal. This is going to be five over seven times seven extra seven fifty plus a fine Time's a eggs to the one fifth plus C, and then the seven cancel and then you're left with five X to the seventy fifth, twelve forty next to the one fifth twelve c, and that is your final anti derivatives.

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