3.10 Integrals 901 to 1000

\(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [901]
\(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [902]
\(\int \genfrac {}{}{}{}{x \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [903]
\(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [904]
\(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x (c+a^2 c x^2)^{3/2}} \, dx\) [905]
\(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [906]
\(\int \genfrac {}{}{}{}{x^4 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [907]
\(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [908]
\(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [909]
\(\int \genfrac {}{}{}{}{x \arctan (a x)^{5/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [910]
\(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [911]
\(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x (c+a^2 c x^2)^{5/2}} \, dx\) [912]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)}{\sqrt {\arctan (a x)}} \, dx\) [913]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)}{\sqrt {\arctan (a x)}} \, dx\) [914]
\(\int \genfrac {}{}{}{}{c+a^2 c x^2}{\sqrt {\arctan (a x)}} \, dx\) [915]
\(\int \genfrac {}{}{}{}{c+a^2 c x^2}{x \sqrt {\arctan (a x)}} \, dx\) [916]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)^2}{\sqrt {\arctan (a x)}} \, dx\) [917]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)^2}{\sqrt {\arctan (a x)}} \, dx\) [918]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2}{\sqrt {\arctan (a x)}} \, dx\) [919]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2}{x \sqrt {\arctan (a x)}} \, dx\) [920]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)^3}{\sqrt {\arctan (a x)}} \, dx\) [921]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)^3}{\sqrt {\arctan (a x)}} \, dx\) [922]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3}{\sqrt {\arctan (a x)}} \, dx\) [923]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3}{x \sqrt {\arctan (a x)}} \, dx\) [924]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2) \sqrt {\arctan (a x)}} \, dx\) [925]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2) \sqrt {\arctan (a x)}} \, dx\) [926]
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2) \sqrt {\arctan (a x)}} \, dx\) [927]
\(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2) \sqrt {\arctan (a x)}} \, dx\) [928]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2)^2 \sqrt {\arctan (a x)}} \, dx\) [929]
\(\int \genfrac {}{}{}{}{x^3}{(c+a^2 c x^2)^2 \sqrt {\arctan (a x)}} \, dx\) [930]
\(\int \genfrac {}{}{}{}{x^2}{(c+a^2 c x^2)^2 \sqrt {\arctan (a x)}} \, dx\) [931]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2)^2 \sqrt {\arctan (a x)}} \, dx\) [932]
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2)^2 \sqrt {\arctan (a x)}} \, dx\) [933]
\(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2)^2 \sqrt {\arctan (a x)}} \, dx\) [934]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [935]
\(\int \genfrac {}{}{}{}{x^5}{(c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [936]
\(\int \genfrac {}{}{}{}{x^4}{(c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [937]
\(\int \genfrac {}{}{}{}{x^3}{(c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [938]
\(\int \genfrac {}{}{}{}{x^2}{(c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [939]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [940]
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [941]
\(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2)^3 \sqrt {\arctan (a x)}} \, dx\) [942]
\(\int \genfrac {}{}{}{}{x^m \sqrt {c+a^2 c x^2}}{\sqrt {\arctan (a x)}} \, dx\) [943]
\(\int \genfrac {}{}{}{}{x \sqrt {c+a^2 c x^2}}{\sqrt {\arctan (a x)}} \, dx\) [944]
\(\int \genfrac {}{}{}{}{\sqrt {c+a^2 c x^2}}{\sqrt {\arctan (a x)}} \, dx\) [945]
\(\int \genfrac {}{}{}{}{\sqrt {c+a^2 c x^2}}{x \sqrt {\arctan (a x)}} \, dx\) [946]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)^{3/2}}{\sqrt {\arctan (a x)}} \, dx\) [947]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)^{3/2}}{\sqrt {\arctan (a x)}} \, dx\) [948]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{3/2}}{\sqrt {\arctan (a x)}} \, dx\) [949]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{3/2}}{x \sqrt {\arctan (a x)}} \, dx\) [950]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)^{5/2}}{\sqrt {\arctan (a x)}} \, dx\) [951]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)^{5/2}}{\sqrt {\arctan (a x)}} \, dx\) [952]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{5/2}}{\sqrt {\arctan (a x)}} \, dx\) [953]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{5/2}}{x \sqrt {\arctan (a x)}} \, dx\) [954]
\(\int \genfrac {}{}{}{}{x^m}{\sqrt {c+a^2 c x^2} \sqrt {\arctan (a x)}} \, dx\) [955]
\(\int \genfrac {}{}{}{}{x}{\sqrt {c+a^2 c x^2} \sqrt {\arctan (a x)}} \, dx\) [956]
\(\int \genfrac {}{}{}{}{1}{\sqrt {c+a^2 c x^2} \sqrt {\arctan (a x)}} \, dx\) [957]
\(\int \genfrac {}{}{}{}{1}{x \sqrt {c+a^2 c x^2} \sqrt {\arctan (a x)}} \, dx\) [958]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2)^{3/2} \sqrt {\arctan (a x)}} \, dx\) [959]
\(\int \genfrac {}{}{}{}{x^2}{(c+a^2 c x^2)^{3/2} \sqrt {\arctan (a x)}} \, dx\) [960]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2)^{3/2} \sqrt {\arctan (a x)}} \, dx\) [961]
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2)^{3/2} \sqrt {\arctan (a x)}} \, dx\) [962]
\(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2)^{3/2} \sqrt {\arctan (a x)}} \, dx\) [963]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2)^{5/2} \sqrt {\arctan (a x)}} \, dx\) [964]
\(\int \genfrac {}{}{}{}{x^4}{(c+a^2 c x^2)^{5/2} \sqrt {\arctan (a x)}} \, dx\) [965]
\(\int \genfrac {}{}{}{}{x^3}{(c+a^2 c x^2)^{5/2} \sqrt {\arctan (a x)}} \, dx\) [966]
\(\int \genfrac {}{}{}{}{x^2}{(c+a^2 c x^2)^{5/2} \sqrt {\arctan (a x)}} \, dx\) [967]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2)^{5/2} \sqrt {\arctan (a x)}} \, dx\) [968]
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2)^{5/2} \sqrt {\arctan (a x)}} \, dx\) [969]
\(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2)^{5/2} \sqrt {\arctan (a x)}} \, dx\) [970]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)}{\arctan (a x)^{3/2}} \, dx\) [971]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)}{\arctan (a x)^{3/2}} \, dx\) [972]
\(\int \genfrac {}{}{}{}{c+a^2 c x^2}{\arctan (a x)^{3/2}} \, dx\) [973]
\(\int \genfrac {}{}{}{}{c+a^2 c x^2}{x \arctan (a x)^{3/2}} \, dx\) [974]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)^2}{\arctan (a x)^{3/2}} \, dx\) [975]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)^2}{\arctan (a x)^{3/2}} \, dx\) [976]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2}{\arctan (a x)^{3/2}} \, dx\) [977]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2}{x \arctan (a x)^{3/2}} \, dx\) [978]
\(\int \genfrac {}{}{}{}{x^m (c+a^2 c x^2)^3}{\arctan (a x)^{3/2}} \, dx\) [979]
\(\int \genfrac {}{}{}{}{x (c+a^2 c x^2)^3}{\arctan (a x)^{3/2}} \, dx\) [980]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3}{\arctan (a x)^{3/2}} \, dx\) [981]
\(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3}{x \arctan (a x)^{3/2}} \, dx\) [982]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2) \arctan (a x)^{3/2}} \, dx\) [983]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2) \arctan (a x)^{3/2}} \, dx\) [984]
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2) \arctan (a x)^{3/2}} \, dx\) [985]
\(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2) \arctan (a x)^{3/2}} \, dx\) [986]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [987]
\(\int \genfrac {}{}{}{}{x^4}{(c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [988]
\(\int \genfrac {}{}{}{}{x^3}{(c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [989]
\(\int \genfrac {}{}{}{}{x^2}{(c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [990]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [991]
\(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [992]
\(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [993]
\(\int \genfrac {}{}{}{}{1}{x^2 (c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [994]
\(\int \genfrac {}{}{}{}{1}{x^3 (c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [995]
\(\int \genfrac {}{}{}{}{1}{x^4 (c+a^2 c x^2)^2 \arctan (a x)^{3/2}} \, dx\) [996]
\(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2)^3 \arctan (a x)^{3/2}} \, dx\) [997]
\(\int \genfrac {}{}{}{}{x^3}{(c+a^2 c x^2)^3 \arctan (a x)^{3/2}} \, dx\) [998]
\(\int \genfrac {}{}{}{}{x^2}{(c+a^2 c x^2)^3 \arctan (a x)^{3/2}} \, dx\) [999]
\(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2)^3 \arctan (a x)^{3/2}} \, dx\) [1000]