I'm trying to find the exact value of

Jewel Beard

Jewel Beard

Answered question

2022-04-06

I'm trying to find the exact value of
133arctan(x2)1+x2dx

Answer & Explanation

pobijedi6wro

pobijedi6wro

Beginner2022-04-07Added 15 answers

Use the substitution x=tanθ to obtain:
I=π6π3arctan(tan2θ)dθ
Since
abf(x)dx=abf(a+bx)dx
We get:
I=π6π3arctan(cot2θ)dθ=π6π3arot(tan2θ)dθ
Add the two to get:
2I=π6π3π2dθI=π224
....which well agrees with Wolfram Alpha.

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