((x^2)+1)^2 using substitution

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Homework Statement


((x^2)+1)^2 integrate using substitution


Homework Equations





3. The attempt at solution
ok so i let u= x^2 + 1
du/dx = 2x
du= 2xdx
where do i go from there
 
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Sidthewall said:

Homework Statement


((x^2)+1)^2 using substitution
Do what with ((x^2)+1)^2 using substitution?
Sidthewall said:

Homework Equations





3. The attempt at solution
ok so i let u= x^2 + 1
du/dx = 2x
du= 2xdx
where do i go from there
 
integrate using substitution, my bad forgot to put that down
 
That's the reason for this:

Homework Statement



So is this it?
\int (x^2 + 1)^2 dx

I wouldn't use substitution for this one.
 
I wouldn't either. I would expand and then solve but the question said to use substitution
 
The substitution u=x2+1 won't help. What substitution does the form x2+1 suggest? Think trig functions.
 
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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