How to evaluate the integral $\int_0^{\infty} e^{-\frac{1}{2}\left(x^2+ \frac{c}{x^2}\right)}dx$?
48686
Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.
85081
$\int_{0}^{\infty} \frac{\cos x - e^{-x}}{x} \mathrm dx$ Evaluate Integral
142619
Evaluating the complex integral $\int_{|z|=2}^{}\frac{1}{z^2+1}dz$
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
138174
Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$
96759
How do you evaluate the integral $\int\frac{x^2-1}{(x^4+3 x^2+1) \tan^{-1}\left(\frac{x^2+1}{x}\right)}\,dx$?
104094
Integral of $\frac{1}{(1+x^2)^2}$
93759
Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$
15569
Integral of the form $\int_0^\infty \exp{\left(-\frac{(a+bx)^2}{x}\right)}\frac{dx}{\sqrt{x^3}}$
97582
How do I evaluate this integral $\int_0^\pi{\frac{{{x^2}}}{{\sqrt 5-2\cos x}}}\operatorname d\!x$?
70013
How to calculate $\int \frac{x^2 }{(x^2+1)^2} dx$?
132369
Evaluating the indefinite integral $\int\log\!\left(x+\sqrt{x^2-1}\right)\!dx$
140203
Find the value of $\int_{-\infty}^{\infty} \frac{e^{-x^2}}{1+x^2} dx$ .
51971
How to evaluate the integral $\int e^{x^3}dx $
111775
$\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
98838
How to evaluate $\int_0^1 \frac{\ln(x+1)}{x^2+1} dx$
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$