query: Evaluate $\int x^3 \sqrt{4-x^2} dx$
positive_passages.docid: 143878
positive_passages.text: Solve: $\int x^3\sqrt{4-x^2}dx$
negative_passages.docid: 122407
negative_passages.text: If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)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: 141711
negative_passages.text: Evaluate the following integral?
negative_passages.docid: 70830
negative_passages.text: How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$?
negative_passages.docid: 91212
negative_passages.text: Evaluate $\int \cos^3 x\;\sin^2 xdx$
negative_passages.docid: 38005
negative_passages.text: Integral of $\sin (x^3)dx$
negative_passages.docid: 152977
negative_passages.text: Integrate $\int\sqrt{x+\sqrt{x^{2}+2}} dx$ .
negative_passages.docid: 150843
negative_passages.text: Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$
negative_passages.docid: 17333
negative_passages.text: Definite Integral $\int_2^4\frac{\sqrt{\log(9-x)}}{\sqrt{\log(9-x)}+\sqrt{\log(3+x)}}dx$
negative_passages.docid: 64800
negative_passages.text: Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $
negative_passages.docid: 137549
negative_passages.text: Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx $
negative_passages.docid: 25509
negative_passages.text: evaluation of an integral involving algebraic numbers
negative_passages.docid: 95934
negative_passages.text: How to integrate $\int\frac{1}{\sqrt{1+x^3}}\mathrm dx$?
negative_passages.docid: 1150
negative_passages.text: Indefinite Integral of $\sqrt{\sin x}$
negative_passages.docid: 145907
negative_passages.text: How do you evaluate this integral $\int \frac{6x^{3}+7x^2-12x+1}{\sqrt{x^2+4x+6}}dx$
negative_passages.docid: 144039
negative_passages.text: Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$