[passer-by]

Question 76

Let $ u= e^x $ and integrand is of the form
$$ \frac{1}{u(u^2+a^2)} = \frac{1}{a^2}(\frac{1}{u}-\frac{u}{u^2+a^2}) $$

Now we can integrate easily.

The answer of this question is $ e^{-2\pi}(\pi-\ln(\sqrt{2})) $


Next question....

Question 77: Evaluate $$ \int_0^{\infty} e^{-x^2}\cos(x) \,\,dx $$