Is My Integration Correct for y' = sinx - 2x4?

Student4
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Can anyone just help me integrate this 2 times. (with maple or somekind math program, or hand).
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Need to see if my 2 solutions is correct. :approve:
 
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Student4 said:
Can anyone just help me integrate this 2 times. (with maple or somekind math program, or hand). Need to see if my 2 solutions is correct for this one. :approve:

View attachment 40636
Show us what you got.
 
y'=sin(x)+2x^4+c
y=-cos(x)-2/5x^5+c
 
the solution should be ...

y' = sinx - 2x4 + c1

y = -cosx - (2/5)x5 + c1x + c2
 
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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