query: I need help solving this integral: $\int_0^1 \frac{\ln{\left(x+\sqrt{1-x^2}\right)}}{x} \ dx = \frac{\pi^A}{B}$
positive_passages.docid: 17996
positive_passages.text: Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
negative_passages.docid: 21464
negative_passages.text: Finding the integral $\int_0^1 \frac{x^a - 1}{\log x} dx$
negative_passages.docid: 27195
negative_passages.text: Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
negative_passages.docid: 140122
negative_passages.text: Integral: $\int_0^1\frac{\mathrm{Li}_2(x^2)}{\sqrt{1-x^2}}dx$
negative_passages.docid: 4971
negative_passages.text: $\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
negative_passages.docid: 8358
negative_passages.text: Prove $\int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2 $
negative_passages.docid: 8289
negative_passages.text: Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$
negative_passages.docid: 6830
negative_passages.text: Find $\int\frac1x\sqrt\frac{1-x}{1+x}\ dx$
negative_passages.docid: 39629
negative_passages.text: Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$
negative_passages.docid: 102649
negative_passages.text: Prove that $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx=\frac{\pi^2}{96}+\frac{\ln^2 2}{8}$
negative_passages.docid: 135519
negative_passages.text: How to approach solving $\int_0^{\pi/2} \ln(a^2 \cos^2 x +b^2 \sin^2 x ) dx$
negative_passages.docid: 145590
negative_passages.text: Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$
negative_passages.docid: 155919
negative_passages.text: Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$
negative_passages.docid: 139784
negative_passages.text: Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
negative_passages.docid: 47452
negative_passages.text: Calculus Question: $\int_0^1\frac{(x-x^2)^4}{1+x^2}dx$
negative_passages.docid: 121310
negative_passages.text: Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$
negative_passages.docid: 93610
negative_passages.text: What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?