query: Computing $\int_{-1}^1(1-x^2)^n\ dx$
positive_passages.docid: 21616
positive_passages.text: Calculate integral $\int_{-1}^{1} (1-x^2)^n dx $
negative_passages.docid: 29383
negative_passages.text: Computing $\int_{-\infty}^{\infty} \frac{\cos x}{x^{2} + a^{2}}dx$ using residue calculus
negative_passages.docid: 67263
negative_passages.text: Compute integral $\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$
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: 139784
negative_passages.text: Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
negative_passages.docid: 87395
negative_passages.text: Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$
negative_passages.docid: 71611
negative_passages.text: Evaluating $\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$
negative_passages.docid: 55094
negative_passages.text: How to show $i^{-1} = -i$?
negative_passages.docid: 69978
negative_passages.text: Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
negative_passages.docid: 157931
negative_passages.text: Contour integration of $\int \frac{dx} {(1+x^2)^{n+1}}$
negative_passages.docid: 104583
negative_passages.text: Simplify $\int \frac{1}{\sqrt{2-x^2}}\, dx$
negative_passages.docid: 93205
negative_passages.text: Compute: $\int_{0}^{1}\frac{x^4+1}{x^6+1} dx$
negative_passages.docid: 75067
negative_passages.text: Compute this integral
negative_passages.docid: 53519
negative_passages.text: Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
negative_passages.docid: 29680
negative_passages.text: How to determine $\int x^2 e^{-x^2}\mathrm dx$?
negative_passages.docid: 17996
negative_passages.text: Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
negative_passages.docid: 91333
negative_passages.text: How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$