Can I do this in this math problem/substitution Calc 2

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Homework Statement


Find integral of 4*e^(4x)*sin(e^(4x))dx

Homework Equations

The Attempt at a Solution


Can I do this in this math problem
I took the integral of 4e^(4x)*sin(e^(4x)) dx using substitution method. in the end I got e^(4x)*-cos*[1/e^(4x)] do the ex^4x just cancel out?
 
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Steebly said:

Homework Statement


Find integral of 4*e^(4x)*sin(e^(4x))dx

Homework Equations

The Attempt at a Solution


Can I do this in this math problem
I took the integral of 4e^(4x)*sin(e^(4x)) dx using substitution method. in the end I got e^(4x)*-cos*[1/e^(4x)] do the ex^4x just cancel out?
Yes.
 
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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