With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that
![I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx](https://tex.z-dn.net/?f=I%20%3D%20%5Cdisplaystyle%20%5Cint_0%5E%5Cinfty%20%5Cfrac%7B%5Csqrt%5B%5Cphi%5D%7Bx%7D%20%5Ctan%5E%7B-1%7D%28x%29%7D%7B%281%2Bx%5E%5Cphi%29%5E2%7D%20%5C%2C%20dx%20%3D%20%5Cint_0%5E%5Cinfty%20%5Cfrac%7Bx%5E%7B%5Cphi-1%7D%20%5Ctan%5E%7B-1%7D%28x%29%7D%7Bx%20%281%2Bx%5E%5Cphi%29%5E2%7D%20%5C%2C%20dx)
Replace
:

Split the integral at x = 1. For the integral over [1, ∞), substitute
:

The integrals involving tan⁻¹ disappear, and we're left with

The correct sum of the polynomial is
.
We have to determine
The correct sum of the polynomials.
<h3>
Sum of the
polynomials</h3>
Sum of the polynomials is just a matter of combining like terms, with some order of operations.
Then,
The correct sum of the polynomial is;

Hence, the correct sum of the polynomial is
.
To know more about the sum of the polynomial click the link is given below.
brainly.com/question/9465649
Answer:
the answer is 23 1/3 or 23 and 1/3 or 23.3 with repeating decimal
Step-by-step explanation:
first find the number that 3 multiplied by a number equals closest to say 70 so 69 leaving 1 amd you use your denominator you divided by and you would have 1/3
Answer: ong
Step-by-step explanation: im straight
I think it’s the last one but I’m not sure