Is My Solution for the Antiderivative of 8x - 3 sec^2x Correct?

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Antiderivatives - 8x - 3 sec^2x

Im not sure whether my answer to this antiderivative question is correct and would like your opinion.

1. The antiderivative statement asks: Find f

2. f prime (x) = 8x - 3 sec^2x
Most general antiderivative = F(x) + C
Antidefferentiation formula: Function = sec^2, Particular antiderivative = tan x


3. My attempt at a solution
= [(8x^2)/2] - 3tan x
= 4x^2 - 3tan x


Is this correct?
 
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looks good to me, nice job.
 
physicsman2 said:
looks good to me, nice job.

Ok, great, thanks.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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