query: Evaluate $\int_{0}^{\infty} \frac{ \sin^{2n+1} x} {x} \text dx $
positive_passages.docid: 24182
positive_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
negative_passages.docid: 138230
negative_passages.text: Evaluate $ \int^{\frac{\pi}{2}}_0 \frac{\sin x}{\sin x+\cos x}\,dx $ using substitution $t=\frac{\pi}{2}-x$
negative_passages.docid: 84884
negative_passages.text: Need help with the integral $\int_{0}^\infty e^{-x^{2}}x^{2n+1}dx $
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
negative_passages.docid: 130967
negative_passages.text: How to show that $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(4x)\cdots\sin(2^kx)\over x^{k+1}}\mathrm dx=2^{0.5(k^2-k-2)}\pi?$
negative_passages.docid: 104904
negative_passages.text: Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.
negative_passages.docid: 3068
negative_passages.text: Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?
negative_passages.docid: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 129734
negative_passages.text: Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
negative_passages.docid: 81621
negative_passages.text: How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
negative_passages.docid: 6014
negative_passages.text: Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
negative_passages.docid: 34855
negative_passages.text: Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$
negative_passages.docid: 64480
negative_passages.text: How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
negative_passages.docid: 65982
negative_passages.text: Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
negative_passages.docid: 112621
negative_passages.text: Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
negative_passages.docid: 100569
negative_passages.text: Evaluating the improper integral $\int_{0}^{\infty} \frac{x^3}{e^{x}-1} dx$
negative_passages.docid: 76333
negative_passages.text: Let $b>0.$ Evaluate $\lim_{n \to \infty} \int^{b}_{0} \frac{\sin nx}{nx}dx$