How to Integrate sqrt(1+3x) Correctly?

sargentidiot
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NVM bout the arc length, need help on integrations

Homework Statement


Integrate sqrt(1+3x)

Homework Equations


Sqrt (1+3x)

The Attempt at a Solution


i made it into
(1+3x)^(1/2)
 
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sargentidiot said:
NVM bout the arc length, need help on integrations

Homework Statement


Integrate sqrt(1+3x)


Homework Equations


Sqrt (1+3x)




The Attempt at a Solution


i made it into
(1+3x)^(1/2)

have you tried u-substitution? use u=1+3x and see what you get
 
ok so i got
(2(1+3x)^(3/2))/9
would that be right
 
sargentidiot said:
ok so i got
(2(1+3x)^(3/2))/9
would that be right

yes, you got it
 
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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