query: Solve $\int_0^1\frac{x^7-1}{\ln x}dx$
positive_passages.docid: 21464
positive_passages.text: Finding the integral $\int_0^1 \frac{x^a - 1}{\log x} dx$
negative_passages.docid: 30459
negative_passages.text: Evaluate $\int^1_0 \log^2(1-x) \log^2(x) \, dx$
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 122361
negative_passages.text: Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$
negative_passages.docid: 41416
negative_passages.text: Integrating $ \int_2^4 \frac{ \sqrt{\ln(9-x)} }{ \sqrt{\ln(9-x)}+\sqrt{\ln(x+3)} } dx. $
negative_passages.docid: 53518
negative_passages.text: Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
negative_passages.docid: 31964
negative_passages.text: Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
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: 67837
negative_passages.text: Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$
negative_passages.docid: 35861
negative_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 54638
negative_passages.text: Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
negative_passages.docid: 44059
negative_passages.text: Evaluating $\int_{-1}^{1}\frac{\arctan{x}}{1+x}\ln{\left(\frac{1+x^2}{2}\right)}dx$
negative_passages.docid: 21616
negative_passages.text: Calculate integral $\int_{-1}^{1} (1-x^2)^n dx $
negative_passages.docid: 26814
negative_passages.text: Solve $\int \frac{1}{\sin ^{\frac{1}{2}}x \cos^{\frac{7}{2}}x}dx$
negative_passages.docid: 115759
negative_passages.text: Evaluating this integral : $ \int \frac {1-7\cos^2x} {\sin^7x \cos^2x} dx $
negative_passages.docid: 50509
negative_passages.text: Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
negative_passages.docid: 147977
negative_passages.text: Evaluate $\int_0^1\left(\frac{x-1}{x+1}\right)^n\frac{1}{\ln x} \,dx$