A "proof" for $0=1$ by integrating $\int \frac{dx}{x\ln x}$ by parts
118577
Fallacious proof involving trigonometry
67837
Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$
139453
Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$
54513
Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
57686
Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
31964
Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
88154
Proving $\int_{0}^1\frac{x-1}{\log x}dx=\log 2$ and $\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$
80710
Does $\int_{-1}^1 \frac 1 x dx$ equal zero?
54638
Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
115089
Definite Integral: $\int_0^1\frac{x^{2} -1}{\log x}\,dx$
136966
Riemann integral proof $\int^b_a f(x) \, dx>0$
45841
integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration?
34762
Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?
83488
Integrating $\ln x$ by parts
98344
Prove that $\int_0^1[f''(x)]^2dx\ge4.$
122971
how to prove that $\ln(1+x)< x$
32672
Integrating :$\int_{0}^{1} \frac{x^{b}-x^{a}}{\log(x)}\sin(\log(x))dx$