query: The integral $\int \sqrt{\ x \sqrt[3]{\ x \sqrt[4]{\ x \sqrt[5]{\ x \cdots}}}} dx$
positive_passages.docid: 146015
positive_passages.text: Computing $\int \sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{x\cdots}}}} \,\mathrm{d}x$
negative_passages.docid: 121406
negative_passages.text: Interesting Integration with respect to $[x]$ where $[\cdot]$ is greatest integer function
negative_passages.docid: 86811
negative_passages.text: Help understanding a concept in multiple integrals
negative_passages.docid: 51488
negative_passages.text: Evaluating $\int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$
negative_passages.docid: 61466
negative_passages.text: what is $\int_{|z|=3}\frac{1}{(z-2)^n(z-4)^m}dz$ for $m,n\in\mathbb{N}$?
negative_passages.docid: 143409
negative_passages.text: Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.
negative_passages.docid: 129521
negative_passages.text: Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
negative_passages.docid: 100869
negative_passages.text: How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$
negative_passages.docid: 99584
negative_passages.text: Evaluation of $\int \frac{\sqrt{\sin ^4x+\cos ^4x}}{\sin ^3x \cos x }dx$
negative_passages.docid: 44653
negative_passages.text: $(\int f_1d\mu)^2+\cdots+(\int f_nd\mu)^2\leq(\int \sqrt{f_1^2+\cdots+f_n^2}d\mu)^2$
negative_passages.docid: 47793
negative_passages.text: Integral $\int_0^1\sqrt{1-x^4}dx$
negative_passages.docid: 82187
negative_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: 109901
negative_passages.text: Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
negative_passages.docid: 126576
negative_passages.text: Most efficient way to integrate $\int_0^\pi \sqrt{4\sin^2 x - 4\sin x + 1}\,dx$?
negative_passages.docid: 88368
negative_passages.text: Evaluating $\int_0^1 \sqrt{1 + x ^4 } \, d x $
negative_passages.docid: 101174
negative_passages.text: A closed form for a triple integral with sines and cosines
negative_passages.docid: 124445
negative_passages.text: Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$