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
Answer:
h(g(0)) = 1 - 3y^2 .
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
if b^2 - 4ac is greater than 0 then there are 2 answers that are not equal to each other, but both are real.
If b^2 - 4ac = 0 then you have two real answers that are equal
The real problem is what happens when b^2 - 4ac is less than 0? In this case the answer is a complex number of the form
a + bi
a - bi
where i is the square root of - 1
Answer:
Exact Form:
72/5
Decimal Form:
14.4
Mixed Number Form:
14 2/5
Step-by-step explanation:
yea thats what i got
Ángel and Jayden we’re at track practice.
The track is 2/5 kilometers around.
* Ángel ran 1 lap in 2 minutes.
* Jayden ran 3 laps in 5 minutes.
How far does Jayden run in one minute?
4 1/6 km
