3.3 Integrals 201 to 300

   \(\int \genfrac {}{}{}{}{e^{-\genfrac {}{}{}{}{2019}{4 x^2}}}{x^2} \, dx\) [201]
   \(\int \sin (\sqrt {x}) \, dx\) [202]
   \(\int \genfrac {}{}{}{}{\sqrt {x}}{1+x} \, dx\) [203]
   \(\int \cos (x) \cos (2 x) \cos (3 x) \, dx\) [204]
   \(\int e^{-x^{2 n}} \, dx\) [205]
   \(\int e \, dx\) [206]
   \(\int \genfrac {}{}{}{}{\sin (19 x)+\sin (20 x)}{\cos (19 x)+\cos (20 x)} \, dx\) [207]
   \(\int e^x (\cos ^2(x)+\cos (x) \sin (x)-\sin ^2(x)) \, dx\) [208]
   \(\int \csc (\genfrac {}{}{}{}{\pi }{4}+x) \sin (x) \, dx\) [209]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{x}+x} \, dx\) [210]
   \(\int x^{1+x^2} (1+2 \log (x)) \, dx\) [211]
   \(\int \genfrac {}{}{}{}{-1+2 x^3}{x (1+x^3)} \, dx\) [212]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {1+x^2}} \, dx\) [213]
   \(\int \genfrac {}{}{}{}{\log (2 x)}{x \log (x)} \, dx\) [214]
   \(\int \genfrac {}{}{}{}{1}{1+e^x} \, dx\) [215]
   \(\int \genfrac {}{}{}{}{\log (x) \log (\log (x))}{x} \, dx\) [216]
   \(\int \log (\genfrac {}{}{}{}{1+x}{1-x}) \, dx\) [217]
   \(\int \genfrac {}{}{}{}{1}{(-1+x)^2+x^2} \, dx\) [218]
   \(\int \sqrt {x \sqrt {x^{3/2}}} \, dx\) [219]
   \(\int \cos ^4(x) (\cos (x)-\sin (x)) \sin ^4(x) (\cos (x)+\sin (x)) \, dx\) [220]
   \(\int \log (1+x^2) \, dx\) [221]
   \(\int \genfrac {}{}{}{}{1+2 x}{1+2 x+2 x^2} \, dx\) [222]
   \(\int \genfrac {}{}{}{}{\arcsin (x)}{x^3} \, dx\) [223]
   \(\int \cos (\cos (x)) \sin (2 x) \, dx\) [224]
   \(\int -\sin (x-\sin (x)) \, dx\) [225]
   \(\int \genfrac {}{}{}{}{1}{1+\tan ^{2 \sqrt {505}}(x)} \, dx\) [226]
   \(\int (1-x)^{2020} x \, dx\) [227]
   \(\int \genfrac {}{}{}{}{\sec ^4(x) \tan (x)}{4+\sec ^4(x)} \, dx\) [228]
   \(\int x^{2 x} (2+2 \log (x)) \, dx\) [229]
   \(\int \sqrt {1-x^2} \, dx\) [230]
   \(\int e^{-x^4} x^5 \, dx\) [231]
   \(\int \genfrac {}{}{}{}{1+\cos (x)}{x+\sin (x)} \, dx\) [232]
   \(\int \genfrac {}{}{}{}{\cot ^{-1}(x)+\arctan (x)}{x} \, dx\) [233]
   \(\int \genfrac {}{}{}{}{\sinh (x)}{\cosh (x)-\sinh (x)} \, dx\) [234]
   \(\int \genfrac {}{}{}{}{x}{\sqrt {-1+x}+\sqrt {1+x}} \, dx\) [235]
   \(\int \cos (x+\cos (x)) \, dx\) [236]
   \(\int x^3 \sin (x^2) \, dx\) [237]
   \(\int \genfrac {}{}{}{}{x}{1-x^4} \, dx\) [238]
   \(\int \text {sech}^2(x) \, dx\) [239]
   \(\int (e^{e^x}-e^{e^x-x}) \, dx\) [240]
   \(\int \sqrt {1-\sqrt {x}} \, dx\) [241]
   \(\int \genfrac {}{}{}{}{x^3}{1+x+\genfrac {}{}{}{}{x^2}{2}+\genfrac {}{}{}{}{x^3}{6}} \, dx\) [242]
   \(\int (-\sin (x-\sin (x))+\sin (x+\sin (x))) \, dx\) [243]
   \(\int (\sec ^5(x) \tan ^2(x)+\sec ^3(x) \tan ^4(x)) \, dx\) [244]
   \(\int (1+\log (x)) \log (\log (x)) \, dx\) [245]
   \(\int (\genfrac {}{}{}{}{1}{1+\cos (x)}+\genfrac {}{}{}{}{1}{1+\cot (x)}+\genfrac {}{}{}{}{1}{1+\csc (x)}+\genfrac {}{}{}{}{1}{1+\sec (x)}+\genfrac {}{}{}{}{1}{1+\sin (x)}+\genfrac {}{}{}{}{1}{1+\tan (x)}) \, dx\) [246]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {x-x^2}} \, dx\) [247]
   \(\int \genfrac {}{}{}{}{1}{1+\cos ^2(x)} \, dx\) [248]
   \(\int \genfrac {}{}{}{}{\log (1+x)}{x^2} \, dx\) [249]
   \(\int \sqrt {1-\arccos (\sin (x))^2} \, dx\) [250]
   \(\int (-2+x) (-1+x) x (1+x) (2+x) \, dx\) [251]
   \(\int \genfrac {}{}{}{}{1+2 x^2+3 x^3}{\sqrt [3]{1+x^3}} \, dx\) [252]
   \(\int \csc ^4(x) \sec ^4(x) \, dx\) [253]
   \(\int \genfrac {}{}{}{}{x+\sin (x)}{1+\cos (x)} \, dx\) [254]
   \(\int \cosh ^2(x) \sinh ^3(x) \, dx\) [255]
   \(\int 3^{2^x} 4^x \, dx\) [256]
   \(\int \genfrac {}{}{}{}{\cos (x)-\sin (x)}{2+\sin (2 x)} \, dx\) [257]
   \(\int \genfrac {}{}{}{}{\sec ^2(1+\log (x))-\tan (1+\log (x))}{x^2} \, dx\) [258]
   \(\int \sqrt {\genfrac {}{}{}{}{\log (\genfrac {}{}{}{}{1}{x})}{x}} \, dx\) [259]
   \(\int (1-\cos (x))^5 \cos (5 x) \, dx\) [260]
   \(\int \genfrac {}{}{}{}{3 \cos (x)+4 \sin (x)}{4 \cos (x)+3 \sin (x)} \, dx\) [261]
   \(\int (-\sqrt {3}-\sqrt {4-x^2}+\sqrt {4-(1+x)^2}) \, dx\) [262]
   \(\int x^2 \sin (\log (x)) \, dx\) [263]
   \(\int e^{-x} (36 x^5-12 x^6+x^7) \, dx\) [264]
   \(\int \arccos (x) \arcsin (x) \, dx\) [265]
   \(\int (1+6 x-7 x^2+4 x^3-x^4)^n \, dx\) [266]
   \(\int \genfrac {}{}{}{}{x^4}{\sqrt {1-x}} \, dx\) [267]
   \(\int \sin (x^{-n}) \, dx\) [268]
   \(\int \genfrac {}{}{}{}{1}{2} (-x+\sqrt {4-3 x^2}) \, dx\) [269]
   \(\int (1-3 x^2+x^4)^n \, dx\) [270]
   \(\int \genfrac {}{}{}{}{(1+e^{-x}) x}{-1+e^x} \, dx\) [271]
   \(\int e^{-x} x^4 \sin (x) \, dx\) [272]
   \(\int \genfrac {}{}{}{}{-3 (-3 x+x^3)+(-3 x+x^3)^3}{\sqrt {-4+x^2}} \, dx\) [273]
   \(\int \genfrac {}{}{}{}{1}{(1+x^2)^3} \, dx\) [274]
   \(\int \log (\sqrt {3}+\tan (x)) \, dx\) [275]
   \(\int \sqrt {(\cos (20 x)+3 \cos (21 x)+\cos (22 x))^2+(\sin (20 x)+3 \sin (21 x)+\sin (22 x))^2} \, dx\) [276]
   \(\int \genfrac {}{}{}{}{e^{-2 x} \sin (3 x)}{x} \, dx\) [277]
   \(\int (1-x)^{2/3} \sqrt [3]{x} \, dx\) [278]
   \(\int e \, dx\) [279]
   \(\int \text {sech}(x) \, dx\) [280]
   \(\int \genfrac {}{}{}{}{e^x}{(1+e^x) \log (1+e^x)} \, dx\) [281]
   \(\int (1-x+x^2-x^3+x^4) (1+x+x^2+x^3+x^4) \, dx\) [282]
   \(\int \genfrac {}{}{}{}{1}{120} (-4+x) (-3+x) (-2+x) (-1+x) x \, dx\) [283]
   \(\int (x+x \cos (x)+\sin (x)+\cos (x) \sin (x)) \, dx\) [284]
   \(\int (\cos ^2(x)+\cot ^2(x)+\csc ^2(x)+\sec ^2(x)+\sin ^2(x)+\tan ^2(x)) \, dx\) [285]
   \(\int e^{\log ^2(x)} (1+2 \log (x)) \, dx\) [286]
   \(\int ((1-x)^3+(x-x^2)^3-3 (1-x) (x-x^2) (-1+x^2)+(-1+x^2)^3) \, dx\) [287]
   \(\int (\cos ^6(x)+3 \cos ^2(x) \sin ^2(x)+\sin ^6(x)) \, dx\) [288]
   \(\int e^x x^e (1+e+x) \, dx\) [289]
   \(\int (\sqrt {2} \sqrt {\genfrac {}{}{}{}{x}{1+x}}+\genfrac {}{}{}{}{x^2}{2-x^2}) \, dx\) [290]
   \(\int \genfrac {}{}{}{}{1+2 x^{2022}}{x+x^{2023}} \, dx\) [291]
   \(\int (3 \cos (23 x) \sin (20 x)+20 \sin (43 x)) \, dx\) [292]
   \(\int \genfrac {}{}{}{}{\sin (x)}{2 e^x+\cos (x)+\sin (x)} \, dx\) [293]
   \(\int \log ^{-\log (e \pi )}(x) \log (\genfrac {}{}{}{}{x}{\pi }) \, dx\) [294]
   \(\int (x+8 x^2+10 x^3+5 x^4+x^5) \, dx\) [295]
   \(\int \genfrac {}{}{}{}{(1+x) (4+x)}{(2+x) (3+x)} \, dx\) [296]
   \(\int x \cot (x) \, dx\) [297]
   \(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{x}+x} (-1-x^2+x^4+x^6)}{x^4} \, dx\) [298]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {(-1+x) (1+x)^3}} \, dx\) [299]
   \(\int x \sin ^4(x) \, dx\) [300]