Calculating indefinite integrals

Cacophony
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Homework Statement


a) S 13(4^x + 3^x)dx
b) S (cosx + sec^2x)dx
c) S (3-(1/x))dx
d) S e^(7x)dx


Homework Equations



The S is supposed to be the integration sign

The Attempt at a Solution



Are these correct or at least close?

a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C

b) = (sinx + tanx) + C

c) = -ln + C

d) Do I use U-substitution for this one?
 
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c) and d) are incorrect. The integral of "3" is "3x". For d), yes, use substitution. Let u= 7x.
 
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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