3.1 Integrals 1 to 50

\(\int \arcsin (x) \log (x) \, dx\) [1]
\(\int \genfrac {}{}{}{}{x \arcsin (x)}{\sqrt {1-x^2}} \, dx\) [2]
\(\int -\arcsin (\sqrt {x}-\sqrt {1+x}) \, dx\) [3]
\(\int \log (1+x \sqrt {1+x^2}) \, dx\) [4]
\(\int \genfrac {}{}{}{}{\cos ^2(x)}{\sqrt {1+\cos ^2(x)+\cos ^4(x)}} \, dx\) [5]
\(\int \tan (x) \sqrt {1+\tan ^4(x)} \, dx\) [6]
\(\int \genfrac {}{}{}{}{\tan (x)}{\sqrt {1+\sec ^3(x)}} \, dx\) [7]
\(\int \sqrt {2+2 \tan (x)+\tan ^2(x)} \, dx\) [8]
\(\int \arctan (\sqrt {-1+\sec (x)}) \sin (x) \, dx\) [9]
\(\int \genfrac {}{}{}{}{e^{\arcsin (x)} x^3}{\sqrt {1-x^2}} \, dx\) [10]
\(\int \genfrac {}{}{}{}{x \log (1+x^2) \log (x+\sqrt {1+x^2})}{\sqrt {1+x^2}} \, dx\) [11]
\(\int \arctan (x+\sqrt {1-x^2}) \, dx\) [12]
\(\int \genfrac {}{}{}{}{x \arctan (x+\sqrt {1-x^2})}{\sqrt {1-x^2}} \, dx\) [13]
\(\int \genfrac {}{}{}{}{\arcsin (x)}{1+\sqrt {1-x^2}} \, dx\) [14]
\(\int \genfrac {}{}{}{}{\log (x+\sqrt {1+x^2})}{(1-x^2)^{3/2}} \, dx\) [15]
\(\int \genfrac {}{}{}{}{\arcsin (x)}{(1+x^2)^{3/2}} \, dx\) [16]
\(\int \genfrac {}{}{}{}{\log (x+\sqrt {-1+x^2})}{(1+x^2)^{3/2}} \, dx\) [17]
\(\int \genfrac {}{}{}{}{\log (x)}{x^2 \sqrt {-1+x^2}} \, dx\) [18]
\(\int \genfrac {}{}{}{}{\sqrt {1+x^3}}{x} \, dx\) [19]
\(\int \genfrac {}{}{}{}{x \log (x+\sqrt {-1+x^2})}{\sqrt {-1+x^2}} \, dx\) [20]
\(\int \genfrac {}{}{}{}{x^3 \arcsin (x)}{\sqrt {1-x^4}} \, dx\) [21]
\(\int \genfrac {}{}{}{}{x^3 \sec ^{-1}(x)}{\sqrt {-1+x^4}} \, dx\) [22]
\(\int \genfrac {}{}{}{}{x \arctan (x) \log (x+\sqrt {1+x^2})}{\sqrt {1+x^2}} \, dx\) [23]
\(\int \genfrac {}{}{}{}{x \log (1+\sqrt {1-x^2})}{\sqrt {1-x^2}} \, dx\) [24]
\(\int \genfrac {}{}{}{}{x \log (x+\sqrt {1+x^2})}{\sqrt {1+x^2}} \, dx\) [25]
\(\int \genfrac {}{}{}{}{x \log (x+\sqrt {1-x^2})}{\sqrt {1-x^2}} \, dx\) [26]
\(\int \genfrac {}{}{}{}{\log (x)}{x^2 \sqrt {1-x^2}} \, dx\) [27]
\(\int \genfrac {}{}{}{}{x \arctan (x)}{\sqrt {1+x^2}} \, dx\) [28]
\(\int \genfrac {}{}{}{}{\arctan (x)}{x^2 \sqrt {1-x^2}} \, dx\) [29]
\(\int \genfrac {}{}{}{}{x \arctan (x)}{\sqrt {1-x^2}} \, dx\) [30]
\(\int \genfrac {}{}{}{}{\arctan (x)}{x^2 \sqrt {1+x^2}} \, dx\) [31]
\(\int \genfrac {}{}{}{}{\arcsin (x)}{x^2 \sqrt {1-x^2}} \, dx\) [32]
\(\int \genfrac {}{}{}{}{x \log (x)}{\sqrt {-1+x^2}} \, dx\) [33]
\(\int \genfrac {}{}{}{}{\log (x)}{x^2 \sqrt {1+x^2}} \, dx\) [34]
\(\int \genfrac {}{}{}{}{x \sec ^{-1}(x)}{\sqrt {-1+x^2}} \, dx\) [35]
\(\int \genfrac {}{}{}{}{x \log (x)}{\sqrt {1+x^2}} \, dx\) [36]
\(\int \genfrac {}{}{}{}{\sin (x)}{1+\sin ^2(x)} \, dx\) [37]
\(\int \genfrac {}{}{}{}{1+x^2}{(1-x^2) \sqrt {1+x^4}} \, dx\) [38]
\(\int \genfrac {}{}{}{}{1-x^2}{(1+x^2) \sqrt {1+x^4}} \, dx\) [39]
\(\int \genfrac {}{}{}{}{\log (\sin (x))}{1+\sin (x)} \, dx\) [40]
\(\int \log (\sin (x)) \sqrt {1+\sin (x)} \, dx\) [41]
\(\int \genfrac {}{}{}{}{\sec (x)}{\sqrt {-1+\sec ^4(x)}} \, dx\) [42]
\(\int \genfrac {}{}{}{}{\tan (x)}{\sqrt {1+\tan ^4(x)}} \, dx\) [43]
\(\int \genfrac {}{}{}{}{\sin (x)}{\sqrt {1-\sin ^6(x)}} \, dx\) [44]
\(\int \sqrt {-\sqrt {-1+\sec (x)}+\sqrt {1+\sec (x)}} \, dx\) [45]
\(\int x \arctan (x)^2 \log (1+x^2) \, dx\) [46]
\(\int \arctan (x \sqrt {1+x^2}) \, dx\) [47]
\(\int -\arctan (\sqrt {x}-\sqrt {1+x}) \, dx\) [48]
\(\int \arcsin (\genfrac {}{}{}{}{x}{\sqrt {1-x^2}}) \, dx\) [49]
\(\int \arctan (x \sqrt {1-x^2}) \, dx\) [50]