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3.13
Integrals 1201 to 1300
3.13.1
\(\int e^{-\text {arctanh}(a x)} x^m \sqrt {c-a^2 c x^2} \, dx\) [1201]
3.13.2
\(\int e^{-\text {arctanh}(a x)} x^2 \sqrt {c-a^2 c x^2} \, dx\) [1202]
3.13.3
\(\int e^{-\text {arctanh}(a x)} x \sqrt {c-a^2 c x^2} \, dx\) [1203]
3.13.4
\(\int e^{-\text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx\) [1204]
3.13.5
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x} \, dx\) [1205]
3.13.6
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^2} \, dx\) [1206]
3.13.7
\(\int e^{-\text {arctanh}(a x)} (c-a^2 c x^2)^{3/2} \, dx\) [1207]
3.13.8
\(\int e^{-\text {arctanh}(a x)} (c-a^2 c x^2)^{5/2} \, dx\) [1208]
3.13.9
\(\int e^{-\text {arctanh}(a x)} (c-a^2 c x^2)^{7/2} \, dx\) [1209]
3.13.10
\(\int e^{-\text {arctanh}(a x)} (c-a^2 c x^2)^{9/2} \, dx\) [1210]
3.13.11
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)}}{\sqrt {c-a^2 c x^2}} \, dx\) [1211]
3.13.12
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)}}{(c-a^2 c x^2)^{3/2}} \, dx\) [1212]
3.13.13
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)}}{(c-a^2 c x^2)^{5/2}} \, dx\) [1213]
3.13.14
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)}}{(c-a^2 c x^2)^{7/2}} \, dx\) [1214]
3.13.15
\(\int e^{-\text {arctanh}(a x)} x^m (c-a^2 c x^2)^p \, dx\) [1215]
3.13.16
\(\int e^{-\text {arctanh}(a x)} x^3 (1-a^2 x^2)^p \, dx\) [1216]
3.13.17
\(\int e^{-\text {arctanh}(a x)} x^2 (1-a^2 x^2)^p \, dx\) [1217]
3.13.18
\(\int e^{-\text {arctanh}(a x)} x (1-a^2 x^2)^p \, dx\) [1218]
3.13.19
\(\int e^{-\text {arctanh}(a x)} (1-a^2 x^2)^p \, dx\) [1219]
3.13.20
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} (1-a^2 x^2)^p}{x} \, dx\) [1220]
3.13.21
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} (1-a^2 x^2)^p}{x^2} \, dx\) [1221]
3.13.22
\(\int e^{-\text {arctanh}(a x)} x^3 (c-a^2 c x^2)^p \, dx\) [1222]
3.13.23
\(\int e^{-\text {arctanh}(a x)} x^2 (c-a^2 c x^2)^p \, dx\) [1223]
3.13.24
\(\int e^{-\text {arctanh}(a x)} x (c-a^2 c x^2)^p \, dx\) [1224]
3.13.25
\(\int e^{-\text {arctanh}(a x)} (c-a^2 c x^2)^p \, dx\) [1225]
3.13.26
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} (c-a^2 c x^2)^p}{x} \, dx\) [1226]
3.13.27
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} (c-a^2 c x^2)^p}{x^2} \, dx\) [1227]
3.13.28
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2)^4 \, dx\) [1228]
3.13.29
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2)^3 \, dx\) [1229]
3.13.30
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2)^2 \, dx\) [1230]
3.13.31
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2) \, dx\) [1231]
3.13.32
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{c-a^2 c x^2} \, dx\) [1232]
3.13.33
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{(c-a^2 c x^2)^2} \, dx\) [1233]
3.13.34
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{(c-a^2 c x^2)^3} \, dx\) [1234]
3.13.35
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{(c-a^2 c x^2)^4} \, dx\) [1235]
3.13.36
\(\int e^{-2 \text {arctanh}(a x)} x^3 \sqrt {c-a^2 c x^2} \, dx\) [1236]
3.13.37
\(\int e^{-2 \text {arctanh}(a x)} x^2 \sqrt {c-a^2 c x^2} \, dx\) [1237]
3.13.38
\(\int e^{-2 \text {arctanh}(a x)} x \sqrt {c-a^2 c x^2} \, dx\) [1238]
3.13.39
\(\int e^{-2 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx\) [1239]
3.13.40
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x} \, dx\) [1240]
3.13.41
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^2} \, dx\) [1241]
3.13.42
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^3} \, dx\) [1242]
3.13.43
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^4} \, dx\) [1243]
3.13.44
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^5} \, dx\) [1244]
3.13.45
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2)^{3/2} \, dx\) [1245]
3.13.46
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2)^{5/2} \, dx\) [1246]
3.13.47
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2)^{7/2} \, dx\) [1247]
3.13.48
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{\sqrt {c-a^2 c x^2}} \, dx\) [1248]
3.13.49
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{(c-a^2 c x^2)^{3/2}} \, dx\) [1249]
3.13.50
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{(c-a^2 c x^2)^{5/2}} \, dx\) [1250]
3.13.51
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)}}{(c-a^2 c x^2)^{7/2}} \, dx\) [1251]
3.13.52
\(\int e^{-2 \text {arctanh}(a x)} x^m \sqrt {c-a^2 c x^2} \, dx\) [1252]
3.13.53
\(\int e^{-2 \text {arctanh}(a x)} (c-a^2 c x^2)^p \, dx\) [1253]
3.13.54
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^4 \, dx\) [1254]
3.13.55
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^3 \, dx\) [1255]
3.13.56
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^2 \, dx\) [1256]
3.13.57
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2) \, dx\) [1257]
3.13.58
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{c-a^2 c x^2} \, dx\) [1258]
3.13.59
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{(c-a^2 c x^2)^2} \, dx\) [1259]
3.13.60
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{(c-a^2 c x^2)^3} \, dx\) [1260]
3.13.61
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{(c-a^2 c x^2)^4} \, dx\) [1261]
3.13.62
\(\int e^{-3 \text {arctanh}(a x)} x^3 \sqrt {c-a^2 c x^2} \, dx\) [1262]
3.13.63
\(\int e^{-3 \text {arctanh}(a x)} x^2 \sqrt {c-a^2 c x^2} \, dx\) [1263]
3.13.64
\(\int e^{-3 \text {arctanh}(a x)} x \sqrt {c-a^2 c x^2} \, dx\) [1264]
3.13.65
\(\int e^{-3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx\) [1265]
3.13.66
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x} \, dx\) [1266]
3.13.67
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^2} \, dx\) [1267]
3.13.68
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^3} \, dx\) [1268]
3.13.69
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^4} \, dx\) [1269]
3.13.70
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^5} \, dx\) [1270]
3.13.71
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^{9/2} \, dx\) [1271]
3.13.72
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^{7/2} \, dx\) [1272]
3.13.73
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^{5/2} \, dx\) [1273]
3.13.74
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^{3/2} \, dx\) [1274]
3.13.75
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{\sqrt {c-a^2 c x^2}} \, dx\) [1275]
3.13.76
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{(c-a^2 c x^2)^{3/2}} \, dx\) [1276]
3.13.77
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{(c-a^2 c x^2)^{5/2}} \, dx\) [1277]
3.13.78
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)}}{(c-a^2 c x^2)^{7/2}} \, dx\) [1278]
3.13.79
\(\int e^{-3 \text {arctanh}(a x)} x^m \sqrt {c-a^2 c x^2} \, dx\) [1279]
3.13.80
\(\int e^{-3 \text {arctanh}(a x)} (c-a^2 c x^2)^p \, dx\) [1280]
3.13.81
\(\int e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} (1-a^2 x^2)^{5/2} \, dx\) [1281]
3.13.82
\(\int e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} (1-a^2 x^2)^{3/2} \, dx\) [1282]
3.13.83
\(\int e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} \sqrt {1-a^2 x^2} \, dx\) [1283]
3.13.84
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{\sqrt {1-a^2 x^2}} \, dx\) [1284]
3.13.85
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(1-a^2 x^2)^{3/2}} \, dx\) [1285]
3.13.86
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(1-a^2 x^2)^{5/2}} \, dx\) [1286]
3.13.87
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(1-a^2 x^2)^{7/2}} \, dx\) [1287]
3.13.88
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(1-a^2 x^2)^{9/2}} \, dx\) [1288]
3.13.89
\(\int e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} (c-a^2 c x^2)^{5/2} \, dx\) [1289]
3.13.90
\(\int e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} (c-a^2 c x^2)^{3/2} \, dx\) [1290]
3.13.91
\(\int e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx\) [1291]
3.13.92
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{\sqrt {c-a^2 c x^2}} \, dx\) [1292]
3.13.93
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(c-a^2 c x^2)^{3/2}} \, dx\) [1293]
3.13.94
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(c-a^2 c x^2)^{5/2}} \, dx\) [1294]
3.13.95
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(c-a^2 c x^2)^{7/2}} \, dx\) [1295]
3.13.96
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(c-a^2 c x^2)^{9/2}} \, dx\) [1296]
3.13.97
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} x^3}{(c-a^2 c x^2)^{5/4}} \, dx\) [1297]
3.13.98
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} x^2}{(c-a^2 c x^2)^{5/4}} \, dx\) [1298]
3.13.99
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)} x}{(c-a^2 c x^2)^{5/4}} \, dx\) [1299]
3.13.100
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} \text {arctanh}(a x)}}{(c-a^2 c x^2)^{5/4}} \, dx\) [1300]
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