[
prev
] [
prev-tail
] [
tail
] [
up
]
3.4
Integrals 301 to 385
3.4.1
\(\int \genfrac {}{}{}{}{e^{5 i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [301]
3.4.2
\(\int \genfrac {}{}{}{}{e^{4 i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [302]
3.4.3
\(\int \genfrac {}{}{}{}{e^{3 i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [303]
3.4.4
\(\int \genfrac {}{}{}{}{e^{2 i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [304]
3.4.5
\(\int \genfrac {}{}{}{}{e^{i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [305]
3.4.6
\(\int \genfrac {}{}{}{}{e^{-i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [306]
3.4.7
\(\int \genfrac {}{}{}{}{e^{-2 i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [307]
3.4.8
\(\int \genfrac {}{}{}{}{e^{-3 i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [308]
3.4.9
\(\int \genfrac {}{}{}{}{e^{-4 i \text {ArcTan}(a x)}}{\sqrt {1+a^2 x^2}} \, dx\) [309]
3.4.10
\(\int \genfrac {}{}{}{}{e^{5 i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [310]
3.4.11
\(\int \genfrac {}{}{}{}{e^{4 i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [311]
3.4.12
\(\int \genfrac {}{}{}{}{e^{3 i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [312]
3.4.13
\(\int \genfrac {}{}{}{}{e^{2 i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [313]
3.4.14
\(\int \genfrac {}{}{}{}{e^{i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [314]
3.4.15
\(\int \genfrac {}{}{}{}{e^{-i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [315]
3.4.16
\(\int \genfrac {}{}{}{}{e^{-2 i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [316]
3.4.17
\(\int \genfrac {}{}{}{}{e^{-3 i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [317]
3.4.18
\(\int \genfrac {}{}{}{}{e^{-4 i \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [318]
3.4.19
\(\int \genfrac {}{}{}{}{e^{5 i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [319]
3.4.20
\(\int \genfrac {}{}{}{}{e^{4 i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [320]
3.4.21
\(\int \genfrac {}{}{}{}{e^{3 i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [321]
3.4.22
\(\int \genfrac {}{}{}{}{e^{2 i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [322]
3.4.23
\(\int \genfrac {}{}{}{}{e^{i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [323]
3.4.24
\(\int \genfrac {}{}{}{}{e^{-i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [324]
3.4.25
\(\int \genfrac {}{}{}{}{e^{-2 i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [325]
3.4.26
\(\int \genfrac {}{}{}{}{e^{-3 i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [326]
3.4.27
\(\int \genfrac {}{}{}{}{e^{-4 i \text {ArcTan}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\) [327]
3.4.28
\(\int \genfrac {}{}{}{}{e^{5 i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [328]
3.4.29
\(\int \genfrac {}{}{}{}{e^{4 i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [329]
3.4.30
\(\int \genfrac {}{}{}{}{e^{3 i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [330]
3.4.31
\(\int \genfrac {}{}{}{}{e^{2 i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [331]
3.4.32
\(\int \genfrac {}{}{}{}{e^{i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [332]
3.4.33
\(\int \genfrac {}{}{}{}{e^{-i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [333]
3.4.34
\(\int \genfrac {}{}{}{}{e^{-2 i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [334]
3.4.35
\(\int \genfrac {}{}{}{}{e^{-3 i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [335]
3.4.36
\(\int \genfrac {}{}{}{}{e^{-4 i \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\) [336]
3.4.37
\(\int e^{n \text {ArcTan}(a x)} (c+a^2 c x^2)^2 \, dx\) [337]
3.4.38
\(\int e^{n \text {ArcTan}(a x)} (c+a^2 c x^2) \, dx\) [338]
3.4.39
\(\int e^{n \text {ArcTan}(a x)} \, dx\) [339]
3.4.40
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^3}{c+a^2 c x^2} \, dx\) [340]
3.4.41
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^2}{c+a^2 c x^2} \, dx\) [341]
3.4.42
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x}{c+a^2 c x^2} \, dx\) [342]
3.4.43
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{c+a^2 c x^2} \, dx\) [343]
3.4.44
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{x (c+a^2 c x^2)} \, dx\) [344]
3.4.45
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{x^2 (c+a^2 c x^2)} \, dx\) [345]
3.4.46
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{x^3 (c+a^2 c x^2)} \, dx\) [346]
3.4.47
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{(c+a^2 c x^2)^4} \, dx\) [347]
3.4.48
\(\int e^{n \text {ArcTan}(a x)} (c+a^2 c x^2)^{3/2} \, dx\) [348]
3.4.49
\(\int e^{n \text {ArcTan}(a x)} \sqrt {c+a^2 c x^2} \, dx\) [349]
3.4.50
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [350]
3.4.51
\(\int e^{n \text {ArcTan}(a x)} x^2 (c+a^2 c x^2)^{3/2} \, dx\) [351]
3.4.52
\(\int e^{n \text {ArcTan}(a x)} x^2 \sqrt {c+a^2 c x^2} \, dx\) [352]
3.4.53
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^3}{\sqrt {c+a^2 c x^2}} \, dx\) [353]
3.4.54
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^2}{\sqrt {c+a^2 c x^2}} \, dx\) [354]
3.4.55
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x}{\sqrt {c+a^2 c x^2}} \, dx\) [355]
3.4.56
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{\sqrt {c+a^2 c x^2}} \, dx\) [356]
3.4.57
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{x \sqrt {c+a^2 c x^2}} \, dx\) [357]
3.4.58
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{x^2 \sqrt {c+a^2 c x^2}} \, dx\) [358]
3.4.59
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{x^3 \sqrt {c+a^2 c x^2}} \, dx\) [359]
3.4.60
\(\int e^{n \text {ArcTan}(a x)} \sqrt [3]{c+a^2 c x^2} \, dx\) [360]
3.4.61
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{\sqrt [3]{c+a^2 c x^2}} \, dx\) [361]
3.4.62
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{2/3}} \, dx\) [362]
3.4.63
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)}}{(c+a^2 c x^2)^{4/3}} \, dx\) [363]
3.4.64
\(\int e^{n \text {ArcTan}(a x)} x^m (c+a^2 c x^2) \, dx\) [364]
3.4.65
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^m}{c+a^2 c x^2} \, dx\) [365]
3.4.66
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^m}{(c+a^2 c x^2)^2} \, dx\) [366]
3.4.67
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^m}{(c+a^2 c x^2)^3} \, dx\) [367]
3.4.68
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^m}{\sqrt {c+a^2 c x^2}} \, dx\) [368]
3.4.69
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^m}{(c+a^2 c x^2)^{3/2}} \, dx\) [369]
3.4.70
\(\int \genfrac {}{}{}{}{e^{n \text {ArcTan}(a x)} x^m}{(c+a^2 c x^2)^{5/2}} \, dx\) [370]
3.4.71
\(\int e^{n \text {ArcTan}(a x)} (c+a^2 c x^2)^p \, dx\) [371]
3.4.72
\(\int e^{-2 i p \text {ArcTan}(a x)} (c+a^2 c x^2)^p \, dx\) [372]
3.4.73
\(\int e^{2 i p \text {ArcTan}(a x)} (c+a^2 c x^2)^p \, dx\) [373]
3.4.74
\(\int e^{i n \text {ArcTan}(a x)} x^2 (c+a^2 c x^2)^{-1-\genfrac {}{}{}{}{n^2}{2}} \, dx\) [374]
3.4.75
\(\int \genfrac {}{}{}{}{e^{6 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^{19}} \, dx\) [375]
3.4.76
\(\int \genfrac {}{}{}{}{e^{4 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^9} \, dx\) [376]
3.4.77
\(\int \genfrac {}{}{}{}{e^{2 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^3} \, dx\) [377]
3.4.78
\(\int \genfrac {}{}{}{}{e^{-2 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^3} \, dx\) [378]
3.4.79
\(\int \genfrac {}{}{}{}{e^{-4 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^9} \, dx\) [379]
3.4.80
\(\int \genfrac {}{}{}{}{e^{5 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^{27/2}} \, dx\) [380]
3.4.81
\(\int \genfrac {}{}{}{}{e^{3 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^{11/2}} \, dx\) [381]
3.4.82
\(\int \genfrac {}{}{}{}{e^{i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^{3/2}} \, dx\) [382]
3.4.83
\(\int \genfrac {}{}{}{}{e^{-i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^{3/2}} \, dx\) [383]
3.4.84
\(\int \genfrac {}{}{}{}{e^{-3 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^{11/2}} \, dx\) [384]
3.4.85
\(\int \genfrac {}{}{}{}{e^{-5 i \text {ArcTan}(a x)} x^2}{(c+a^2 c x^2)^{27/2}} \, dx\) [385]
[
prev
] [
prev-tail
] [
front
] [
up
]