3.11 Integrals 1001 to 1100

\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x^3 \sqrt {c-a^2 c x^2}} \, dx\) [1001]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x^4 \sqrt {c-a^2 c x^2}} \, dx\) [1002]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^5}{(c-a^2 c x^2)^{3/2}} \, dx\) [1003]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^4}{(c-a^2 c x^2)^{3/2}} \, dx\) [1004]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^3}{(c-a^2 c x^2)^{3/2}} \, dx\) [1005]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^2}{(c-a^2 c x^2)^{3/2}} \, dx\) [1006]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x}{(c-a^2 c x^2)^{3/2}} \, dx\) [1007]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{(c-a^2 c x^2)^{3/2}} \, dx\) [1008]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x (c-a^2 c x^2)^{3/2}} \, dx\) [1009]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x^2 (c-a^2 c x^2)^{3/2}} \, dx\) [1010]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x^3 (c-a^2 c x^2)^{3/2}} \, dx\) [1011]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x^4 (c-a^2 c x^2)^{3/2}} \, dx\) [1012]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^6}{(c-a^2 c x^2)^{5/2}} \, dx\) [1013]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^5}{(c-a^2 c x^2)^{5/2}} \, dx\) [1014]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^4}{(c-a^2 c x^2)^{5/2}} \, dx\) [1015]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^3}{(c-a^2 c x^2)^{5/2}} \, dx\) [1016]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^2}{(c-a^2 c x^2)^{5/2}} \, dx\) [1017]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x}{(c-a^2 c x^2)^{5/2}} \, dx\) [1018]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{(c-a^2 c x^2)^{5/2}} \, dx\) [1019]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x (c-a^2 c x^2)^{5/2}} \, dx\) [1020]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x^2 (c-a^2 c x^2)^{5/2}} \, dx\) [1021]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{x^3 (c-a^2 c x^2)^{5/2}} \, dx\) [1022]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{(c-a^2 c x^2)^{7/2}} \, dx\) [1023]
\(\int e^{\text {arctanh}(a x)} x^m (c-a^2 c x^2)^2 \, dx\) [1024]
\(\int e^{\text {arctanh}(a x)} x^m (c-a^2 c x^2) \, dx\) [1025]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{c-a^2 c x^2} \, dx\) [1026]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{(c-a^2 c x^2)^2} \, dx\) [1027]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{(c-a^2 c x^2)^3} \, dx\) [1028]
\(\int e^{\text {arctanh}(a x)} x^m (1-a^2 x^2)^{5/2} \, dx\) [1029]
\(\int e^{\text {arctanh}(a x)} x^m (1-a^2 x^2)^{3/2} \, dx\) [1030]
\(\int e^{\text {arctanh}(a x)} x^m \sqrt {1-a^2 x^2} \, dx\) [1031]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{\sqrt {1-a^2 x^2}} \, dx\) [1032]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{(1-a^2 x^2)^{3/2}} \, dx\) [1033]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{(1-a^2 x^2)^{5/2}} \, dx\) [1034]
\(\int e^{\text {arctanh}(a x)} x^m (c-a^2 c x^2)^{5/2} \, dx\) [1035]
\(\int e^{\text {arctanh}(a x)} x^m (c-a^2 c x^2)^{3/2} \, dx\) [1036]
\(\int e^{\text {arctanh}(a x)} x^m \sqrt {c-a^2 c x^2} \, dx\) [1037]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{\sqrt {c-a^2 c x^2}} \, dx\) [1038]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{(c-a^2 c x^2)^{3/2}} \, dx\) [1039]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} x^m}{(c-a^2 c x^2)^{5/2}} \, dx\) [1040]
\(\int e^{\text {arctanh}(a x)} x^m (c-a^2 c x^2)^p \, dx\) [1041]
\(\int e^{\text {arctanh}(a x)} x^3 (1-a^2 x^2)^p \, dx\) [1042]
\(\int e^{\text {arctanh}(a x)} x^2 (1-a^2 x^2)^p \, dx\) [1043]
\(\int e^{\text {arctanh}(a x)} x (1-a^2 x^2)^p \, dx\) [1044]
\(\int e^{\text {arctanh}(a x)} (1-a^2 x^2)^p \, dx\) [1045]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} (1-a^2 x^2)^p}{x} \, dx\) [1046]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} (1-a^2 x^2)^p}{x^2} \, dx\) [1047]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} (1-a^2 x^2)^p}{x^3} \, dx\) [1048]
\(\int e^{\text {arctanh}(a x)} x^3 (c-a^2 c x^2)^p \, dx\) [1049]
\(\int e^{\text {arctanh}(a x)} x^2 (c-a^2 c x^2)^p \, dx\) [1050]
\(\int e^{\text {arctanh}(a x)} x (c-a^2 c x^2)^p \, dx\) [1051]
\(\int e^{\text {arctanh}(a x)} (c-a^2 c x^2)^p \, dx\) [1052]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} (c-a^2 c x^2)^p}{x} \, dx\) [1053]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} (c-a^2 c x^2)^p}{x^2} \, dx\) [1054]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} (c-a^2 c x^2)^p}{x^3} \, dx\) [1055]
\(\int e^{2 \text {arctanh}(a x)} x^4 (c-a^2 c x^2) \, dx\) [1056]
\(\int e^{2 \text {arctanh}(a x)} x^3 (c-a^2 c x^2) \, dx\) [1057]
\(\int e^{2 \text {arctanh}(a x)} x^2 (c-a^2 c x^2) \, dx\) [1058]
\(\int e^{2 \text {arctanh}(a x)} x (c-a^2 c x^2) \, dx\) [1059]
\(\int e^{2 \text {arctanh}(a x)} (c-a^2 c x^2) \, dx\) [1060]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)}{x} \, dx\) [1061]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)}{x^2} \, dx\) [1062]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)}{x^3} \, dx\) [1063]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)}{x^4} \, dx\) [1064]
\(\int e^{2 \text {arctanh}(a x)} x^4 (c-a^2 c x^2)^2 \, dx\) [1065]
\(\int e^{2 \text {arctanh}(a x)} x^3 (c-a^2 c x^2)^2 \, dx\) [1066]
\(\int e^{2 \text {arctanh}(a x)} x^2 (c-a^2 c x^2)^2 \, dx\) [1067]
\(\int e^{2 \text {arctanh}(a x)} x (c-a^2 c x^2)^2 \, dx\) [1068]
\(\int e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^2 \, dx\) [1069]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^2}{x} \, dx\) [1070]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^2}{x^2} \, dx\) [1071]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^2}{x^3} \, dx\) [1072]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^2}{x^4} \, dx\) [1073]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^2}{x^5} \, dx\) [1074]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^2}{x^6} \, dx\) [1075]
\(\int e^{2 \text {arctanh}(a x)} x^4 (c-a^2 c x^2)^3 \, dx\) [1076]
\(\int e^{2 \text {arctanh}(a x)} x^3 (c-a^2 c x^2)^3 \, dx\) [1077]
\(\int e^{2 \text {arctanh}(a x)} x^2 (c-a^2 c x^2)^3 \, dx\) [1078]
\(\int e^{2 \text {arctanh}(a x)} x (c-a^2 c x^2)^3 \, dx\) [1079]
\(\int e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^3 \, dx\) [1080]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^3}{x} \, dx\) [1081]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^3}{x^2} \, dx\) [1082]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^3}{x^3} \, dx\) [1083]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^3}{x^4} \, dx\) [1084]
\(\int e^{2 \text {arctanh}(a x)} (c-a^2 c x^2)^4 \, dx\) [1085]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x^4}{c-a^2 c x^2} \, dx\) [1086]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x^3}{c-a^2 c x^2} \, dx\) [1087]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x^2}{c-a^2 c x^2} \, dx\) [1088]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x}{c-a^2 c x^2} \, dx\) [1089]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{c-a^2 c x^2} \, dx\) [1090]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{x (c-a^2 c x^2)} \, dx\) [1091]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{x^2 (c-a^2 c x^2)} \, dx\) [1092]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{x^3 (c-a^2 c x^2)} \, dx\) [1093]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{x^4 (c-a^2 c x^2)} \, dx\) [1094]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x^4}{(c-a^2 c x^2)^2} \, dx\) [1095]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x^3}{(c-a^2 c x^2)^2} \, dx\) [1096]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x^2}{(c-a^2 c x^2)^2} \, dx\) [1097]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} x}{(c-a^2 c x^2)^2} \, dx\) [1098]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{(c-a^2 c x^2)^2} \, dx\) [1099]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{x (c-a^2 c x^2)^2} \, dx\) [1100]