Closed form definite integral: which is closest to answer?

Calculus Level 3

$\int_0^{\infty } \frac{1}{\sqrt[4]{\cosh (x)+7}} \, dx$ has a closed form integral.

None of the supplied, multiple choices is correct. One of the fractions is distinctly closer to the correct value than the others. That fraction is the answer to this problem.

The closed form integral will be given in the solution.

494347/127769 494343/127769 494344/127769 494348/127769 494342/127769 494345/127769 494346/127769

1 solution

A Former Brilliant Member
Nov 28, 2019

$\frac{\sqrt[4]{6} \Gamma \left(\frac{1}{4}\right)^2}{3 \sqrt{\pi }}$

$\frac{494344}{127769}$ is the closest.

Note that a closed form solution is not required to answer this problem; just a numeric answer which is close enough to make the distinction.

Closed form definite integral: which is closest to answer?

1 solution

0 pending reports