Seeking Starting Point for $f(a) = \int_0^1 \frac{\ln\left(ax^2 + 1\right)}{x + 1}\:dx$
52982
Efficient/faster methods to find the general closed form of $\int _0^1\frac{\ln \left(ax^2+b\right)}{x+1}\:dx$
34790
Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
45841
integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration?
139784
Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
24832
Integrating $\frac{1}{\sqrt{ax^2+bx+c}}$ for $a<0$
132388
Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$
101289
Studying the equation $\ln(x)- 1+ x^2=0$
53518
Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
48881
Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
132747
How can one show that $ f(0)\ln(\frac{b}{a})=\lim_{\epsilon\rightarrow 0}\int_{\epsilon a}^{\epsilon b} \frac{f(x)}{x}dx$?
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
151344
Finding $\int_{0}^{1}\int_{0}^{1}\int_{0}^{1} \left\{\frac{x}{y}\right\} \left\{\frac{y}{z}\right\}\left\{\frac{z}{x}\right\} dx\space dy\space dz $
58616
A generalization for Serret's integral $\int_0^a \frac{\ln(1+ax)}{1+x^2}dx$
64800
Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $
113045
How do I find the inverse of $f(x) = \frac{x}{x^2 + 1}$
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$