Question

Find out whether the function converges or dierges, and if the function converges, then integrate the given equation

integrate from 0 to +infinity
sin^2(x) / (x^6+1) dx

Answer 1

\[\int\limits_{0}^{\infty} \sin^2x/(x^6+1) dx\]

Answer 2

Is this problem from a complex analysis course?

Answer 3

That is what Mathematica gave
\[
\int_0^{\infty } \frac{\sin ^2(x)}{x^6+1} \, dx=-\frac{\pi \left(1+e
\left(-2 e+\sqrt{3} \sin \left(\sqrt{3}\right)+\cos
\left(\sqrt{3}\right)\right)\right)}{12 e^2}
\]