3.12.1 \(\int \genfrac {}{}{}{}{1}{x^4 (c+a^2 c x^2)^{3/2} \arctan (a x)^{5/2}} \, dx\) [1101]
3.12.2 \(\int \genfrac {}{}{}{}{x^m}{(c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1102]
3.12.3 \(\int \genfrac {}{}{}{}{x^3}{(c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1103]
3.12.4 \(\int \genfrac {}{}{}{}{x^2}{(c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1104]
3.12.5 \(\int \genfrac {}{}{}{}{x}{(c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1105]
3.12.6 \(\int \genfrac {}{}{}{}{1}{(c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1106]
3.12.7 \(\int \genfrac {}{}{}{}{1}{x (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1107]
3.12.8 \(\int \genfrac {}{}{}{}{1}{x^2 (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1108]
3.12.9 \(\int \genfrac {}{}{}{}{1}{x^3 (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1109]
3.12.10 \(\int \genfrac {}{}{}{}{1}{x^4 (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}} \, dx\) [1110]
3.12.11 \(\int \genfrac {}{}{}{}{x \arctan (a x)^n}{c+a^2 c x^2} \, dx\) [1111]
3.12.12 \(\int \genfrac {}{}{}{}{\arctan (a x)^n}{c+a^2 c x^2} \, dx\) [1112]
3.12.13 \(\int (f x)^m (d+c^2 d x^2)^q (a+b \arctan (c x))^p \, dx\) [1113]
3.12.14 \(\int x^3 (d+e x^2) (a+b \arctan (c x)) \, dx\) [1114]
3.12.15 \(\int x^2 (d+e x^2) (a+b \arctan (c x)) \, dx\) [1115]
3.12.16 \(\int x (d+e x^2) (a+b \arctan (c x)) \, dx\) [1116]
3.12.17 \(\int (d+e x^2) (a+b \arctan (c x)) \, dx\) [1117]
3.12.18 \(\int \genfrac {}{}{}{}{(d+e x^2) (a+b \arctan (c x))}{x} \, dx\) [1118]
3.12.19 \(\int \genfrac {}{}{}{}{(d+e x^2) (a+b \arctan (c x))}{x^2} \, dx\) [1119]
3.12.20 \(\int \genfrac {}{}{}{}{(d+e x^2) (a+b \arctan (c x))}{x^3} \, dx\) [1120]
3.12.21 \(\int \genfrac {}{}{}{}{(d+e x^2) (a+b \arctan (c x))}{x^4} \, dx\) [1121]
3.12.22 \(\int \genfrac {}{}{}{}{(d+e x^2) (a+b \arctan (c x))}{x^5} \, dx\) [1122]
3.12.23 \(\int \genfrac {}{}{}{}{(d+e x^2) (a+b \arctan (c x))}{x^6} \, dx\) [1123]
3.12.24 \(\int \genfrac {}{}{}{}{(d+e x^2) (a+b \arctan (c x))}{x^7} \, dx\) [1124]
3.12.25 \(\int x^3 (d+e x^2)^2 (a+b \arctan (c x)) \, dx\) [1125]
3.12.26 \(\int x^2 (d+e x^2)^2 (a+b \arctan (c x)) \, dx\) [1126]
3.12.27 \(\int x (d+e x^2)^2 (a+b \arctan (c x)) \, dx\) [1127]
3.12.28 \(\int (d+e x^2)^2 (a+b \arctan (c x)) \, dx\) [1128]
3.12.29 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x} \, dx\) [1129]
3.12.30 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x^2} \, dx\) [1130]
3.12.31 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x^3} \, dx\) [1131]
3.12.32 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x^4} \, dx\) [1132]
3.12.33 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x^5} \, dx\) [1133]
3.12.34 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x^6} \, dx\) [1134]
3.12.35 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x^7} \, dx\) [1135]
3.12.36 \(\int \genfrac {}{}{}{}{(d+e x^2)^2 (a+b \arctan (c x))}{x^8} \, dx\) [1136]
3.12.37 \(\int x^3 (d+e x^2)^3 (a+b \arctan (c x)) \, dx\) [1137]
3.12.38 \(\int x^2 (d+e x^2)^3 (a+b \arctan (c x)) \, dx\) [1138]
3.12.39 \(\int x (d+e x^2)^3 (a+b \arctan (c x)) \, dx\) [1139]
3.12.40 \(\int (d+e x^2)^3 (a+b \arctan (c x)) \, dx\) [1140]
3.12.41 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x} \, dx\) [1141]
3.12.42 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^2} \, dx\) [1142]
3.12.43 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^3} \, dx\) [1143]
3.12.44 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^4} \, dx\) [1144]
3.12.45 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^5} \, dx\) [1145]
3.12.46 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^6} \, dx\) [1146]
3.12.47 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^7} \, dx\) [1147]
3.12.48 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^8} \, dx\) [1148]
3.12.49 \(\int \genfrac {}{}{}{}{(d+e x^2)^3 (a+b \arctan (c x))}{x^9} \, dx\) [1149]
3.12.50 \(\int (c+d x^2)^4 \arctan (a x) \, dx\) [1150]
3.12.51 \(\int \genfrac {}{}{}{}{x^3 (a+b \arctan (c x))}{d+e x^2} \, dx\) [1151]
3.12.52 \(\int \genfrac {}{}{}{}{x (a+b \arctan (c x))}{d+e x^2} \, dx\) [1152]
3.12.53 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x (d+e x^2)} \, dx\) [1153]
3.12.54 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x^3 (d+e x^2)} \, dx\) [1154]
3.12.55 \(\int \genfrac {}{}{}{}{x^2 (a+b \arctan (c x))}{d+e x^2} \, dx\) [1155]
3.12.56 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{d+e x^2} \, dx\) [1156]
3.12.57 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x^2 (d+e x^2)} \, dx\) [1157]
3.12.58 \(\int \genfrac {}{}{}{}{x^3 (a+b \arctan (c x))}{(d+e x^2)^2} \, dx\) [1158]
3.12.59 \(\int \genfrac {}{}{}{}{x (a+b \arctan (c x))}{(d+e x^2)^2} \, dx\) [1159]
3.12.60 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x (d+e x^2)^2} \, dx\) [1160]
3.12.61 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x^3 (d+e x^2)^2} \, dx\) [1161]
3.12.62 \(\int \genfrac {}{}{}{}{x^2 (a+b \arctan (c x))}{(d+e x^2)^2} \, dx\) [1162]
3.12.63 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{(d+e x^2)^2} \, dx\) [1163]
3.12.64 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x^2 (d+e x^2)^2} \, dx\) [1164]
3.12.65 \(\int \genfrac {}{}{}{}{x^5 (a+b \arctan (c x))}{(d+e x^2)^3} \, dx\) [1165]
3.12.66 \(\int \genfrac {}{}{}{}{x^3 (a+b \arctan (c x))}{(d+e x^2)^3} \, dx\) [1166]
3.12.67 \(\int \genfrac {}{}{}{}{x (a+b \arctan (c x))}{(d+e x^2)^3} \, dx\) [1167]
3.12.68 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x (d+e x^2)^3} \, dx\) [1168]
3.12.69 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x^3 (d+e x^2)^3} \, dx\) [1169]
3.12.70 \(\int \genfrac {}{}{}{}{x^2 (a+b \arctan (c x))}{(d+e x^2)^3} \, dx\) [1170]
3.12.71 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{(d+e x^2)^3} \, dx\) [1171]
3.12.72 \(\int \genfrac {}{}{}{}{a+b \arctan (c x)}{x^2 (d+e x^2)^3} \, dx\) [1172]
3.12.73 \(\int x^3 \sqrt {d+e x^2} (a+b \arctan (c x)) \, dx\) [1173]
3.12.74 \(\int x^2 \sqrt {d+e x^2} (a+b \arctan (c x)) \, dx\) [1174]
3.12.75 \(\int x \sqrt {d+e x^2} (a+b \arctan (c x)) \, dx\) [1175]
3.12.76 \(\int \sqrt {d+e x^2} (a+b \arctan (c x)) \, dx\) [1176]
3.12.77 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2} (a+b \arctan (c x))}{x} \, dx\) [1177]
3.12.78 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2} (a+b \arctan (c x))}{x^2} \, dx\) [1178]
3.12.79 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2} (a+b \arctan (c x))}{x^3} \, dx\) [1179]
3.12.80 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2} (a+b \arctan (c x))}{x^4} \, dx\) [1180]
3.12.81 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2} (a+b \arctan (c x))}{x^5} \, dx\) [1181]
3.12.82 \(\int \genfrac {}{}{}{}{\sqrt {d+e x^2} (a+b \arctan (c x))}{x^6} \, dx\) [1182]
3.12.83 \(\int x^3 (d+e x^2)^{3/2} (a+b \arctan (c x)) \, dx\) [1183]
3.12.84 \(\int x^2 (d+e x^2)^{3/2} (a+b \arctan (c x)) \, dx\) [1184]
3.12.85 \(\int x (d+e x^2)^{3/2} (a+b \arctan (c x)) \, dx\) [1185]
3.12.86 \(\int (d+e x^2)^{3/2} (a+b \arctan (c x)) \, dx\) [1186]
3.12.87 \(\int \genfrac {}{}{}{}{(d+e x^2)^{3/2} (a+b \arctan (c x))}{x} \, dx\) [1187]
3.12.88 \(\int \genfrac {}{}{}{}{(d+e x^2)^{3/2} (a+b \arctan (c x))}{x^2} \, dx\) [1188]
3.12.89 \(\int \genfrac {}{}{}{}{(d+e x^2)^{3/2} (a+b \arctan (c x))}{x^3} \, dx\) [1189]
3.12.90 \(\int \genfrac {}{}{}{}{(d+e x^2)^{3/2} (a+b \arctan (c x))}{x^4} \, dx\) [1190]
3.12.91 \(\int \genfrac {}{}{}{}{(d+e x^2)^{3/2} (a+b \arctan (c x))}{x^5} \, dx\) [1191]
3.12.92 \(\int \genfrac {}{}{}{}{(d+e x^2)^{3/2} (a+b \arctan (c x))}{x^6} \, dx\) [1192]
3.12.93 \(\int x^3 (d+e x^2)^{5/2} (a+b \arctan (c x)) \, dx\) [1193]
3.12.94 \(\int x^2 (d+e x^2)^{5/2} (a+b \arctan (c x)) \, dx\) [1194]
3.12.95 \(\int x (d+e x^2)^{5/2} (a+b \arctan (c x)) \, dx\) [1195]
3.12.96 \(\int (d+e x^2)^{5/2} (a+b \arctan (c x)) \, dx\) [1196]
3.12.97 \(\int \genfrac {}{}{}{}{(d+e x^2)^{5/2} (a+b \arctan (c x))}{x} \, dx\) [1197]
3.12.98 \(\int \genfrac {}{}{}{}{(d+e x^2)^{5/2} (a+b \arctan (c x))}{x^2} \, dx\) [1198]
3.12.99 \(\int \genfrac {}{}{}{}{(d+e x^2)^{5/2} (a+b \arctan (c x))}{x^3} \, dx\) [1199]
3.12.100 \(\int \genfrac {}{}{}{}{(d+e x^2)^{5/2} (a+b \arctan (c x))}{x^4} \, dx\) [1200]