Improper integral of $\int_0^\infty \frac{e^{-ax} - e^{-bx}}{x}\ dx$
67622
Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
31792
show that $\int_{0}^{\infty}\frac{x\cos ax}{\sinh x}dx=\frac{\pi^2}{4} \operatorname{sech}^2 \left(\frac{a\pi}{2}\right) $
31964
Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
93759
Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$
21375
The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
124463
Integral from $0$ to $\infty$ of $\ln(x)/e^x$
8934
How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
65982
Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
138355
Improper rational/trig integral comes out to $\pi/e$
90095
Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$
145183
finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis
86712
Use rectangular contour to integrate $\int_{0}^{\infty}\frac{\sin(ax)}{e^{2\pi x}-1}dx$
97039
Use integral test to show that Gaussian Integral $\int_{-\infty}^{\infty} e^{-x^2} \ dx$ converges?
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
40537
How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$