How would you compute for the definite integral

Zoie Phillips

Zoie Phillips

Answered question

2022-03-30

How would you compute for the definite integral of
0dx(1+x2)4

Answer & Explanation

Tristatex9tw

Tristatex9tw

Beginner2022-03-31Added 18 answers

The method given below works in general for any integral of the form
0dx(1+x2)n
Plug in x=tan(θ). The integral becomes
0dx(1+x2)4=0π2sec2(θ)dθ(1+tan2(θ))4
=0π2cos6(θ)dθ
=563412π2
=532π
kaosimqu5t

kaosimqu5t

Beginner2022-04-01Added 10 answers

F(u)0dxμ+x2=μ120dx1+x2
=12πμ12
F(μ)=3!0dx(μ+x2)4}=12πd3μ12dμ3
=12π(12)(32)(52)μ72
Set μ=1 in both members:
0dx(1+x2)4=15π66
=532π

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