query: Integrate $ I(t)=\int_0^\infty \left( \frac{\sin tx}{x} \right)^n\,\mathrm d x$
positive_passages.docid: 15324
positive_passages.text: A sine integral $\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$
negative_passages.docid: 144039
negative_passages.text: Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
negative_passages.docid: 114956
negative_passages.text: Integrate $\int \cos^4 x\,\mathrm dx.$
negative_passages.docid: 96191
negative_passages.text: Integral $\int_0^{\infty} \sin(x^2)/x^2\,dx$
negative_passages.docid: 71742
negative_passages.text: integrate $\int_0^{2\pi} e^{\cos \theta} \cos( \sin \theta) d\theta$
negative_passages.docid: 21375
negative_passages.text: The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
negative_passages.docid: 24182
negative_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
negative_passages.docid: 67322
negative_passages.text: evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
negative_passages.docid: 76129
negative_passages.text: Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
negative_passages.docid: 69124
negative_passages.text: Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
negative_passages.docid: 15569
negative_passages.text: Integral of the form $\int_0^\infty \exp{\left(-\frac{(a+bx)^2}{x}\right)}\frac{dx}{\sqrt{x^3}}$
negative_passages.docid: 21857
negative_passages.text: Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$
negative_passages.docid: 60572
negative_passages.text: Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus
negative_passages.docid: 177
negative_passages.text: How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
negative_passages.docid: 67622
negative_passages.text: Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$
negative_passages.docid: 101587
negative_passages.text: Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
negative_passages.docid: 122361
negative_passages.text: Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$