query: Definite Integral $\int_2^4\frac{\sqrt{\log(9-x)}}{\sqrt{\log(9-x)}+\sqrt{\log(3+x)}}dx$
positive_passages.docid: 82187
positive_passages.text: A Putnam Integral $\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$
negative_passages.docid: 2487
negative_passages.text: Integral $\int \frac{\mathrm{d}x}{\sqrt{x}+\sqrt{x+1}+\sqrt{x+2}}$
negative_passages.docid: 115089
negative_passages.text: Definite Integral: $\int_0^1\frac{x^{2} -1}{\log x}\,dx$
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 133922
negative_passages.text: How to solve this integral? $I=\int{e^x \Big(2\log x+\frac{1}{x}+\frac{1}{x^2}\Big)dx}$
negative_passages.docid: 146349
negative_passages.text: $\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
negative_passages.docid: 91955
negative_passages.text: Integral of $\int\frac{1}{\log x}dx$
negative_passages.docid: 109385
negative_passages.text: Evaluating the integral $\int_{-\ln 2}^{\ln 2} e^{-x}(\sin x+x)^{1/3}dx$
negative_passages.docid: 91306
negative_passages.text: Integration of $\frac{1}{\log(x)}$
negative_passages.docid: 53519
negative_passages.text: Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
negative_passages.docid: 65337
negative_passages.text: Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$
negative_passages.docid: 55738
negative_passages.text: Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$
negative_passages.docid: 32672
negative_passages.text: Integrating :$\int_{0}^{1} \frac{x^{b}-x^{a}}{\log(x)}\sin(\log(x))dx$
negative_passages.docid: 49944
negative_passages.text: Integral $\int_1^3 \frac{\log x}{x^2+3}dx$
negative_passages.docid: 137060
negative_passages.text: Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
negative_passages.docid: 108396
negative_passages.text: Integral $\int_0^{\infty} \frac{\log x}{\cosh^2x} \ \mathrm{d}x = \log\frac {\pi}4- \gamma$
negative_passages.docid: 83325
negative_passages.text: Integral of $\frac{\sqrt{x^2+1}}{x}$