If $\int_{-\infty}^\infty f(x) dx = 1$, then what is the value of $\int_{-\infty}^\infty f\left(x-\frac1{x}\right)dx$?
8829
How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$
123802
Is the integral of $\frac{1}{x}$ equal to $\ln(x)$ or $\ln(|x|)$?
34762
Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?
124026
Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$
67622
Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
1392
$\int_{0}^{\infty}{\left(x^3\cdot(e^x-1)^{-1} \right)}dx$
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
45806
Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
40881
Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$
112778
Let $f(x) = x^3-\frac{3}{2}x^2+x+\frac{1}{4}.$ Then the value of $ \int^{3/4}_{1/4}f(f(x))\mathrm dx$
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
31660
Integral $\int_{0}^{1}\left\{\frac{1}{x}\right\}\left\{\frac{1}{1-x}\right\}\left\{1-\frac{1}{x}\right\} d x=?$
68241
Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
76400
Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$