Determine whether the following integrals are convergen: \int_5^\infty\frac{\arctan x}{x^2+3x+5}dx

fortdefruitI

fortdefruitI

Answered question

2021-05-18

Determine whether the following integrals are convergen:
5arctanxx2+3x+5dx

Answer & Explanation

coffentw

coffentw

Skilled2021-05-19Added 103 answers

Solution:
5arctanxx2+3x+5dx
Let an and bn be two sequence such that far n, anbn
π2arctan(x)π2
5arctannn2+3n+5π2n2+3n+5
Now,
an=51n2+3n+5
an=51n2
an=51n2 - Converges

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