query: How to find $\int_0^2\frac{\arctan x}{x^2+2x+2}\,dx$?
positive_passages.docid: 142365
positive_passages.text: Use of substitution into the integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$
negative_passages.docid: 69803
negative_passages.text: An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$
negative_passages.docid: 145521
negative_passages.text: Why does $\arctan(x)= \frac{1}{2i}\log \left( \frac{x-i}{x+i}\right)+k$?
negative_passages.docid: 120953
negative_passages.text: Show that, $2\arctan\left(\frac{1}{3}\right)+2\arcsin\left(\frac{1}{5\sqrt2}\right)-\arctan\left(\frac{1}{7}\right)=\frac{\pi}{4}$
negative_passages.docid: 132388
negative_passages.text: Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$
negative_passages.docid: 103757
negative_passages.text: how can I prove that $\frac{\arctan x}{x }< 1$?
negative_passages.docid: 102156
negative_passages.text: Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx
negative_passages.docid: 19216
negative_passages.text: Proving that $\arctan(x)+\arctan(1/x)=\pm \pi/2$, could this line of reasoning possibly be correct?
negative_passages.docid: 123899
negative_passages.text: $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
negative_passages.docid: 145590
negative_passages.text: Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$
negative_passages.docid: 20016
negative_passages.text: How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$?
negative_passages.docid: 64480
negative_passages.text: How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
negative_passages.docid: 83801
negative_passages.text: Finding $\int \frac {dx}{\sqrt {x^2 + 16}}$
negative_passages.docid: 141387
negative_passages.text: Reduction Integration of $I_n=\int{\frac{x^n}{\sqrt{x^2+a^2}} dx}$
negative_passages.docid: 8642
negative_passages.text: Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $
negative_passages.docid: 4971
negative_passages.text: $\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
negative_passages.docid: 98741
negative_passages.text: Finding $\int_{0}^{\frac{\pi}{4}} \frac{\tan \theta - \tan^3 \theta}{\ln \tan \theta}$