3.2.1 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+x}{(1-\sqrt {3}+x) \sqrt {1+x^3}} \, dx\) [101]
3.2.2 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-x}{(1-\sqrt {3}-x) \sqrt {1-x^3}} \, dx\) [102]
3.2.3 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-x}{(1-\sqrt {3}-x) \sqrt {-1+x^3}} \, dx\) [103]
3.2.4 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+x}{(1-\sqrt {3}+x) \sqrt {-1-x^3}} \, dx\) [104]
3.2.5 \(\int \genfrac {}{}{}{}{(1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\) [105]
3.2.6 \(\int \genfrac {}{}{}{}{(1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\) [106]
3.2.7 \(\int \genfrac {}{}{}{}{(1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\) [107]
3.2.8 \(\int \genfrac {}{}{}{}{(1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\) [108]
3.2.9 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1-\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {a+b x^3}} \, dx\) [109]
3.2.10 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1-\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {a-b x^3}} \, dx\) [110]
3.2.11 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1-\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {-a+b x^3}} \, dx\) [111]
3.2.12 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1-\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {-a-b x^3}} \, dx\) [112]
3.2.13 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+x}{(1+\sqrt {3}+x) \sqrt {1+x^3}} \, dx\) [113]
3.2.14 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-x}{(1+\sqrt {3}-x) \sqrt {1-x^3}} \, dx\) [114]
3.2.15 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-x}{(1+\sqrt {3}-x) \sqrt {-1+x^3}} \, dx\) [115]
3.2.16 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+x}{(1+\sqrt {3}+x) \sqrt {-1-x^3}} \, dx\) [116]
3.2.17 \(\int \genfrac {}{}{}{}{(1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\) [117]
3.2.18 \(\int \genfrac {}{}{}{}{(1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\) [118]
3.2.19 \(\int \genfrac {}{}{}{}{(1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\) [119]
3.2.20 \(\int \genfrac {}{}{}{}{(1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\) [120]
3.2.21 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1+\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {a+b x^3}} \, dx\) [121]
3.2.22 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1+\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {a-b x^3}} \, dx\) [122]
3.2.23 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1+\sqrt {3}-\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {-a+b x^3}} \, dx\) [123]
3.2.24 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x}{(1+\sqrt {3}+\sqrt [3]{\genfrac {}{}{}{}{b}{a}} x) \sqrt {-a-b x^3}} \, dx\) [124]
3.2.25 \(\int \genfrac {}{}{}{}{1+x}{(1+\sqrt {3}+x) \sqrt {1+x^3}} \, dx\) [125]
3.2.26 \(\int \genfrac {}{}{}{}{1+x}{(1-\sqrt {3}+x) \sqrt {1+x^3}} \, dx\) [126]
3.2.27 \(\int \genfrac {}{}{}{}{e+f x}{(1+\sqrt {3}+x) \sqrt {1+x^3}} \, dx\) [127]
3.2.28 \(\int \genfrac {}{}{}{}{e+f x}{(1+\sqrt {3}-x) \sqrt {1-x^3}} \, dx\) [128]
3.2.29 \(\int \genfrac {}{}{}{}{e+f x}{(1+\sqrt {3}-x) \sqrt {-1+x^3}} \, dx\) [129]
3.2.30 \(\int \genfrac {}{}{}{}{e+f x}{(1+\sqrt {3}+x) \sqrt {-1-x^3}} \, dx\) [130]
3.2.31 \(\int \genfrac {}{}{}{}{e+f x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\) [131]
3.2.32 \(\int \genfrac {}{}{}{}{e+f x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\) [132]
3.2.33 \(\int \genfrac {}{}{}{}{e+f x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\) [133]
3.2.34 \(\int \genfrac {}{}{}{}{e+f x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\) [134]
3.2.35 \(\int \genfrac {}{}{}{}{x}{(1+\sqrt {3}+x) \sqrt {1+x^3}} \, dx\) [135]
3.2.36 \(\int \genfrac {}{}{}{}{x}{(1+\sqrt {3}-x) \sqrt {1-x^3}} \, dx\) [136]
3.2.37 \(\int \genfrac {}{}{}{}{x}{(1+\sqrt {3}-x) \sqrt {-1+x^3}} \, dx\) [137]
3.2.38 \(\int \genfrac {}{}{}{}{x}{(1+\sqrt {3}+x) \sqrt {-1-x^3}} \, dx\) [138]
3.2.39 \(\int \genfrac {}{}{}{}{x}{(1-\sqrt {3}+x) \sqrt {1+x^3}} \, dx\) [139]
3.2.40 \(\int \genfrac {}{}{}{}{x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\) [140]
3.2.41 \(\int \genfrac {}{}{}{}{x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\) [141]
3.2.42 \(\int \genfrac {}{}{}{}{x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\) [142]
3.2.43 \(\int \genfrac {}{}{}{}{x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\) [143]
3.2.44 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+x}{(c+d x) \sqrt {1+x^3}} \, dx\) [144]
3.2.45 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-x}{(c+d x) \sqrt {1-x^3}} \, dx\) [145]
3.2.46 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-x}{(c+d x) \sqrt {-1+x^3}} \, dx\) [146]
3.2.47 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+x}{(c+d x) \sqrt {-1-x^3}} \, dx\) [147]
3.2.48 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+x}{(c+d x) \sqrt {1+x^3}} \, dx\) [148]
3.2.49 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-x}{(c+d x) \sqrt {1-x^3}} \, dx\) [149]
3.2.50 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-x}{(c+d x) \sqrt {-1+x^3}} \, dx\) [150]
3.2.51 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+x}{(c+d x) \sqrt {-1-x^3}} \, dx\) [151]
3.2.52 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+x}{x \sqrt {1+x^3}} \, dx\) [152]
3.2.53 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-x}{x \sqrt {1-x^3}} \, dx\) [153]
3.2.54 \(\int \genfrac {}{}{}{}{1+\sqrt {3}-x}{x \sqrt {-1+x^3}} \, dx\) [154]
3.2.55 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+x}{x \sqrt {-1-x^3}} \, dx\) [155]
3.2.56 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+x}{x \sqrt {1+x^3}} \, dx\) [156]
3.2.57 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-x}{x \sqrt {1-x^3}} \, dx\) [157]
3.2.58 \(\int \genfrac {}{}{}{}{1-\sqrt {3}-x}{x \sqrt {-1+x^3}} \, dx\) [158]
3.2.59 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+x}{x \sqrt {-1-x^3}} \, dx\) [159]
3.2.60 \(\int \genfrac {}{}{}{}{x}{(3+x) \sqrt {1+x^3}} \, dx\) [160]
3.2.61 \(\int \genfrac {}{}{}{}{x}{(3+x) \sqrt {1-x^3}} \, dx\) [161]
3.2.62 \(\int \genfrac {}{}{}{}{x}{(3+x) \sqrt {-1+x^3}} \, dx\) [162]
3.2.63 \(\int \genfrac {}{}{}{}{x}{(3+x) \sqrt {-1-x^3}} \, dx\) [163]
3.2.64 \(\int \genfrac {}{}{}{}{e+f x}{(c+d x) \sqrt {1+x^3}} \, dx\) [164]
3.2.65 \(\int \genfrac {}{}{}{}{e+f x}{(c+d x) \sqrt {1-x^3}} \, dx\) [165]
3.2.66 \(\int \genfrac {}{}{}{}{e+f x}{(c+d x) \sqrt {-1+x^3}} \, dx\) [166]
3.2.67 \(\int \genfrac {}{}{}{}{e+f x}{(c+d x) \sqrt {-1-x^3}} \, dx\) [167]
3.2.68 \(\int \genfrac {}{}{}{}{e+f x}{x \sqrt {1+x^3}} \, dx\) [168]
3.2.69 \(\int \genfrac {}{}{}{}{e+f x}{x \sqrt {1-x^3}} \, dx\) [169]
3.2.70 \(\int \genfrac {}{}{}{}{e+f x}{x \sqrt {-1+x^3}} \, dx\) [170]
3.2.71 \(\int \genfrac {}{}{}{}{e+f x}{x \sqrt {-1-x^3}} \, dx\) [171]
3.2.72 \(\int \genfrac {}{}{}{}{c-d x}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\) [172]
3.2.73 \(\int \genfrac {}{}{}{}{e+f x}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\) [173]
3.2.74 \(\int x^2 (a+b x)^n (c+d x^3) \, dx\) [174]
3.2.75 \(\int x (a+b x)^n (c+d x^3) \, dx\) [175]
3.2.76 \(\int (a+b x)^n (c+d x^3) \, dx\) [176]
3.2.77 \(\int \genfrac {}{}{}{}{(a+b x)^n (c+d x^3)}{x} \, dx\) [177]
3.2.78 \(\int x^2 (a+b x)^n (c+d x^3)^2 \, dx\) [178]
3.2.79 \(\int x (a+b x)^n (c+d x^3)^2 \, dx\) [179]
3.2.80 \(\int (a+b x)^n (c+d x^3)^2 \, dx\) [180]
3.2.81 \(\int \genfrac {}{}{}{}{(a+b x)^n (c+d x^3)^2}{x} \, dx\) [181]
3.2.82 \(\int x^2 (a+b x)^n (c+d x^3)^3 \, dx\) [182]
3.2.83 \(\int x (a+b x)^n (c+d x^3)^3 \, dx\) [183]
3.2.84 \(\int (a+b x)^n (c+d x^3)^3 \, dx\) [184]
3.2.85 \(\int \genfrac {}{}{}{}{(a+b x)^n (c+d x^3)^3}{x} \, dx\) [185]
3.2.86 \(\int \genfrac {}{}{}{}{x^5 (e+f x)^n}{a+b x^3} \, dx\) [186]
3.2.87 \(\int \genfrac {}{}{}{}{x^4 (e+f x)^n}{a+b x^3} \, dx\) [187]
3.2.88 \(\int \genfrac {}{}{}{}{x^3 (e+f x)^n}{a+b x^3} \, dx\) [188]
3.2.89 \(\int \genfrac {}{}{}{}{x^2 (e+f x)^n}{a+b x^3} \, dx\) [189]
3.2.90 \(\int \genfrac {}{}{}{}{x (e+f x)^n}{a+b x^3} \, dx\) [190]
3.2.91 \(\int \genfrac {}{}{}{}{(e+f x)^n}{a+b x^3} \, dx\) [191]
3.2.92 \(\int \genfrac {}{}{}{}{(e+f x)^n}{x (a+b x^3)} \, dx\) [192]
3.2.93 \(\int \genfrac {}{}{}{}{(e+f x)^n}{x^2 (a+b x^3)} \, dx\) [193]
3.2.94 \(\int \genfrac {}{}{}{}{x^2 (c+d x)^{1+n}}{a+b x^3} \, dx\) [194]
3.2.95 \(\int \genfrac {}{}{}{}{x^m (e+f x)^n}{a+b x^3} \, dx\) [195]
3.2.96 \(\int \genfrac {}{}{}{}{\sqrt {c+d x^3}}{a+b x} \, dx\) [196]
3.2.97 \(\int \genfrac {}{}{}{}{(d^3+e^3 x^3)^p}{d+e x} \, dx\) [197]
3.2.98 \(\int \genfrac {}{}{}{}{2-2 x-x^2}{(2+x^2) \sqrt {1+x^3}} \, dx\) [198]
3.2.99 \(\int \genfrac {}{}{}{}{2+2 x-x^2}{(2+x^2) \sqrt {1-x^3}} \, dx\) [199]
3.2.100 \(\int \genfrac {}{}{}{}{2+2 x-x^2}{(2+x^2) \sqrt {-1+x^3}} \, dx\) [200]