3.9.1 \(\int \genfrac {}{}{}{}{\sqrt {c+a^2 c x^2} \arctan (a x)^{3/2}}{x} \, dx\) [801]
3.9.2 \(\int x^m (c+a^2 c x^2)^{3/2} \arctan (a x)^{3/2} \, dx\) [802]
3.9.3 \(\int x^2 (c+a^2 c x^2)^{3/2} \arctan (a x)^{3/2} \, dx\) [803]
3.9.4 \(\int x (c+a^2 c x^2)^{3/2} \arctan (a x)^{3/2} \, dx\) [804]
3.9.5 \(\int (c+a^2 c x^2)^{3/2} \arctan (a x)^{3/2} \, dx\) [805]
3.9.6 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{3/2} \arctan (a x)^{3/2}}{x} \, dx\) [806]
3.9.7 \(\int x^m (c+a^2 c x^2)^{5/2} \arctan (a x)^{3/2} \, dx\) [807]
3.9.8 \(\int x^2 (c+a^2 c x^2)^{5/2} \arctan (a x)^{3/2} \, dx\) [808]
3.9.9 \(\int x (c+a^2 c x^2)^{5/2} \arctan (a x)^{3/2} \, dx\) [809]
3.9.10 \(\int (c+a^2 c x^2)^{5/2} \arctan (a x)^{3/2} \, dx\) [810]
3.9.11 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{5/2} \arctan (a x)^{3/2}}{x} \, dx\) [811]
3.9.12 \(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [812]
3.9.13 \(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [813]
3.9.14 \(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [814]
3.9.15 \(\int \genfrac {}{}{}{}{x \arctan (a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [815]
3.9.16 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [816]
3.9.17 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x \sqrt {c+a^2 c x^2}} \, dx\) [817]
3.9.18 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x^2 \sqrt {c+a^2 c x^2}} \, dx\) [818]
3.9.19 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x^3 \sqrt {c+a^2 c x^2}} \, dx\) [819]
3.9.20 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x^4 \sqrt {c+a^2 c x^2}} \, dx\) [820]
3.9.21 \(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [821]
3.9.22 \(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [822]
3.9.23 \(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [823]
3.9.24 \(\int \genfrac {}{}{}{}{x \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [824]
3.9.25 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{(c+a^2 c x^2)^{3/2}} \, dx\) [825]
3.9.26 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x (c+a^2 c x^2)^{3/2}} \, dx\) [826]
3.9.27 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x^2 (c+a^2 c x^2)^{3/2}} \, dx\) [827]
3.9.28 \(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [828]
3.9.29 \(\int \genfrac {}{}{}{}{x^5 \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [829]
3.9.30 \(\int \genfrac {}{}{}{}{x^4 \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [830]
3.9.31 \(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [831]
3.9.32 \(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [832]
3.9.33 \(\int \genfrac {}{}{}{}{x \arctan (a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [833]
3.9.34 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{(c+a^2 c x^2)^{5/2}} \, dx\) [834]
3.9.35 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x (c+a^2 c x^2)^{5/2}} \, dx\) [835]
3.9.36 \(\int \genfrac {}{}{}{}{\arctan (a x)^{3/2}}{x^2 (c+a^2 c x^2)^{5/2}} \, dx\) [836]
3.9.37 \(\int x^m (c+a^2 c x^2) \arctan (a x)^{5/2} \, dx\) [837]
3.9.38 \(\int x^2 (c+a^2 c x^2) \arctan (a x)^{5/2} \, dx\) [838]
3.9.39 \(\int x (c+a^2 c x^2) \arctan (a x)^{5/2} \, dx\) [839]
3.9.40 \(\int (c+a^2 c x^2) \arctan (a x)^{5/2} \, dx\) [840]
3.9.41 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2) \arctan (a x)^{5/2}}{x} \, dx\) [841]
3.9.42 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2) \arctan (a x)^{5/2}}{x^2} \, dx\) [842]
3.9.43 \(\int x^m (c+a^2 c x^2)^2 \arctan (a x)^{5/2} \, dx\) [843]
3.9.44 \(\int x^2 (c+a^2 c x^2)^2 \arctan (a x)^{5/2} \, dx\) [844]
3.9.45 \(\int x (c+a^2 c x^2)^2 \arctan (a x)^{5/2} \, dx\) [845]
3.9.46 \(\int (c+a^2 c x^2)^2 \arctan (a x)^{5/2} \, dx\) [846]
3.9.47 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2 \arctan (a x)^{5/2}}{x} \, dx\) [847]
3.9.48 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^2 \arctan (a x)^{5/2}}{x^2} \, dx\) [848]
3.9.49 \(\int x^m (c+a^2 c x^2)^3 \arctan (a x)^{5/2} \, dx\) [849]
3.9.50 \(\int x^2 (c+a^2 c x^2)^3 \arctan (a x)^{5/2} \, dx\) [850]
3.9.51 \(\int x (c+a^2 c x^2)^3 \arctan (a x)^{5/2} \, dx\) [851]
3.9.52 \(\int (c+a^2 c x^2)^3 \arctan (a x)^{5/2} \, dx\) [852]
3.9.53 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3 \arctan (a x)^{5/2}}{x} \, dx\) [853]
3.9.54 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^3 \arctan (a x)^{5/2}}{x^2} \, dx\) [854]
3.9.55 \(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{5/2}}{c+a^2 c x^2} \, dx\) [855]
3.9.56 \(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{5/2}}{c+a^2 c x^2} \, dx\) [856]
3.9.57 \(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{5/2}}{c+a^2 c x^2} \, dx\) [857]
3.9.58 \(\int \genfrac {}{}{}{}{x \arctan (a x)^{5/2}}{c+a^2 c x^2} \, dx\) [858]
3.9.59 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{c+a^2 c x^2} \, dx\) [859]
3.9.60 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x (c+a^2 c x^2)} \, dx\) [860]
3.9.61 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x^2 (c+a^2 c x^2)} \, dx\) [861]
3.9.62 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x^3 (c+a^2 c x^2)} \, dx\) [862]
3.9.63 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x^4 (c+a^2 c x^2)} \, dx\) [863]
3.9.64 \(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [864]
3.9.65 \(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [865]
3.9.66 \(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [866]
3.9.67 \(\int \genfrac {}{}{}{}{x \arctan (a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [867]
3.9.68 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{(c+a^2 c x^2)^2} \, dx\) [868]
3.9.69 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x (c+a^2 c x^2)^2} \, dx\) [869]
3.9.70 \(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [870]
3.9.71 \(\int \genfrac {}{}{}{}{x^5 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [871]
3.9.72 \(\int \genfrac {}{}{}{}{x^4 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [872]
3.9.73 \(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [873]
3.9.74 \(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [874]
3.9.75 \(\int \genfrac {}{}{}{}{x \arctan (a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [875]
3.9.76 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{(c+a^2 c x^2)^3} \, dx\) [876]
3.9.77 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x (c+a^2 c x^2)^3} \, dx\) [877]
3.9.78 \(\int x^m \sqrt {c+a^2 c x^2} \arctan (a x)^{5/2} \, dx\) [878]
3.9.79 \(\int x^2 \sqrt {c+a^2 c x^2} \arctan (a x)^{5/2} \, dx\) [879]
3.9.80 \(\int x \sqrt {c+a^2 c x^2} \arctan (a x)^{5/2} \, dx\) [880]
3.9.81 \(\int \sqrt {c+a^2 c x^2} \arctan (a x)^{5/2} \, dx\) [881]
3.9.82 \(\int \genfrac {}{}{}{}{\sqrt {c+a^2 c x^2} \arctan (a x)^{5/2}}{x} \, dx\) [882]
3.9.83 \(\int x^m (c+a^2 c x^2)^{3/2} \arctan (a x)^{5/2} \, dx\) [883]
3.9.84 \(\int x^2 (c+a^2 c x^2)^{3/2} \arctan (a x)^{5/2} \, dx\) [884]
3.9.85 \(\int x (c+a^2 c x^2)^{3/2} \arctan (a x)^{5/2} \, dx\) [885]
3.9.86 \(\int (c+a^2 c x^2)^{3/2} \arctan (a x)^{5/2} \, dx\) [886]
3.9.87 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{3/2} \arctan (a x)^{5/2}}{x} \, dx\) [887]
3.9.88 \(\int x^m (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2} \, dx\) [888]
3.9.89 \(\int x^2 (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2} \, dx\) [889]
3.9.90 \(\int x (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2} \, dx\) [890]
3.9.91 \(\int (c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2} \, dx\) [891]
3.9.92 \(\int \genfrac {}{}{}{}{(c+a^2 c x^2)^{5/2} \arctan (a x)^{5/2}}{x} \, dx\) [892]
3.9.93 \(\int \genfrac {}{}{}{}{x^m \arctan (a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [893]
3.9.94 \(\int \genfrac {}{}{}{}{x^3 \arctan (a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [894]
3.9.95 \(\int \genfrac {}{}{}{}{x^2 \arctan (a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [895]
3.9.96 \(\int \genfrac {}{}{}{}{x \arctan (a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [896]
3.9.97 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{\sqrt {c+a^2 c x^2}} \, dx\) [897]
3.9.98 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x \sqrt {c+a^2 c x^2}} \, dx\) [898]
3.9.99 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x^2 \sqrt {c+a^2 c x^2}} \, dx\) [899]
3.9.100 \(\int \genfrac {}{}{}{}{\arctan (a x)^{5/2}}{x^3 \sqrt {c+a^2 c x^2}} \, dx\) [900]