I'm very rusty with calculus, and I was hoping someone would be willing to help me with the following definite integral:
$\int_b^{\infty} \frac{\cos(ax)}{1+x^2} dx$
$b>0$
Thanks in advance.
I'm very rusty with calculus, and I was hoping someone would be willing to help me with the following definite integral:
$\int_b^{\infty} \frac{\cos(ax)}{1+x^2} dx$
$b>0$
Thanks in advance.
For $b = 0$ or $b = -\infty$ you can use contour integration. For other $b$ (assuming $a \neq 0$), you will have to do it numerically.
(If there were a formula in terms of $b$, you would have an elementary formula for an antiderivative of the integrand (just differentiate your formula with respect to $b$ and you'll recover the negative of the integrand!), but there is no elementary formula for an antiderivative of this integrand, I believe).