query: How can one show the multiple integral $\int_{0}^{a} \int_{0}^{a} \frac{dx ~ dy}{(a^2+x^2+y^2)^{3/2}}= \frac{\pi}{6a}$ by hand?
positive_passages.docid: 17337
positive_passages.text: Double Integral $\int\limits_0^a\int\limits_0^a\frac{dx\,dy}{(x^2+y^2+a^2)^\frac32}$
negative_passages.docid: 120388
negative_passages.text: Evaluate $\int\frac{1}{1+x^6} \,dx$
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: 16800
negative_passages.text: Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$
negative_passages.docid: 49306
negative_passages.text: Calculation of $\int_0^{\pi} \frac{\sin^2 x}{a^2+b^2-2ab \cos x}\mathrm dx$
negative_passages.docid: 65847
negative_passages.text: To evaluate $\int_{0}^\pi \frac {\sin^2 x}{a^2-2ab \cos x + b^2}\mathrm dx$?
negative_passages.docid: 146870
negative_passages.text: Integrals depending on a parameter: $\int_{0}^{\pi/2} \ln(a^2\sin^2{x} + \cos^2{x})dx $
negative_passages.docid: 46706
negative_passages.text: Integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$
negative_passages.docid: 21464
negative_passages.text: Finding the integral $\int_0^1 \frac{x^a - 1}{\log x} dx$
negative_passages.docid: 123694
negative_passages.text: How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
negative_passages.docid: 67830
negative_passages.text: Evalute the definite integral: $\int_{0}^{3} (x^2+1) d[x]$
negative_passages.docid: 76408
negative_passages.text: Show that $\int_0^\pi f(\sin x)\,\mathrm{d}x = 2\int_0^{\pi/2}f(\sin x) \, \mathrm{d}x$
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 108554
negative_passages.text: Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
negative_passages.docid: 120899
negative_passages.text: Integration with a constant "a": $ \int_0^a \frac1{\sqrt {a^2-x^2}} dx $
negative_passages.docid: 109316
negative_passages.text: How to calculate $\int_0^{\pi/2} \sin^a x \cos^b x \,\mathrm{d} x$
negative_passages.docid: 102156
negative_passages.text: Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx