Find ##f(x)## in the problem involving integration

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Homework Statement
see attached
Relevant Equations
integration
Q. 3(b).

This is a textbook problem; unless i am missing something ...the textbook solution is wrong!

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solution;

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Mythoughts;

##f(x)=2\cos 3x-3\sin 3x## ...by using the product rule on ##\dfrac{d}{dx} (e^{2x} \cos 3x)##.
 

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Your solution seems fine.
 
Please get in the habit of posting full problem statements without expressing them exclusively with pictures.
 
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nuuskur said:
Please get in the habit of posting full problem statements without expressing them exclusively with pictures.
Noted.
 
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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