3.1.1 \(\int \frac {1}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\)
  3.1.2 \(\int \frac {1}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\)
  3.1.3 \(\int \frac {1}{(c+d x) (2 c^3+d^3 x^3)^{2/3}} \, dx\)
  3.1.4 \(\int \frac {1}{(1+\sqrt [3]{2} x) (1+x^3)^{2/3}} \, dx\)
  3.1.5 \(\int \frac {1}{(1-\sqrt [3]{2} x) (1-x^3)^{2/3}} \, dx\)
  3.1.6 \(\int \frac {2^{2/3}-2 x}{(2^{2/3}+x) \sqrt {1+x^3}} \, dx\)
  3.1.7 \(\int \frac {2^{2/3}+2 x}{(2^{2/3}-x) \sqrt {1-x^3}} \, dx\)
  3.1.8 \(\int \frac {2^{2/3}+2 x}{(2^{2/3}-x) \sqrt {-1+x^3}} \, dx\)
  3.1.9 \(\int \frac {2^{2/3}-2 x}{(2^{2/3}+x) \sqrt {-1-x^3}} \, dx\)
  3.1.10 \(\int \frac {2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\)
  3.1.11 \(\int \frac {2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\)
  3.1.12 \(\int \frac {2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\)
  3.1.13 \(\int \frac {2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{(2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\)
  3.1.14 \(\int \frac {c-2 d x}{(c+d x) \sqrt {c^3+4 d^3 x^3}} \, dx\)
  3.1.15 \(\int \frac {1+x}{(2-x) \sqrt {1+x^3}} \, dx\)
  3.1.16 \(\int \frac {1-x}{(2+x) \sqrt {1-x^3}} \, dx\)
  3.1.17 \(\int \frac {1-x}{(2+x) \sqrt {-1+x^3}} \, dx\)
  3.1.18 \(\int \frac {1+x}{(2-x) \sqrt {-1-x^3}} \, dx\)
  3.1.19 \(\int \frac {\sqrt [3]{a}+\sqrt [3]{b} x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\)
  3.1.20 \(\int \frac {\sqrt [3]{a}-\sqrt [3]{b} x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\)
  3.1.21 \(\int \frac {\sqrt [3]{a}-\sqrt [3]{b} x}{(2 \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\)
  3.1.22 \(\int \frac {\sqrt [3]{a}+\sqrt [3]{b} x}{(2 \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\)
  3.1.23 \(\int \frac {c-2 d x}{(c+d x) \sqrt {c^3-8 d^3 x^3}} \, dx\)
  3.1.24 \(\int \frac {1+\sqrt {3}+x}{(1-\sqrt {3}+x) \sqrt {1+x^3}} \, dx\)
  3.1.25 \(\int \frac {1+\sqrt {3}-x}{(1-\sqrt {3}-x) \sqrt {1-x^3}} \, dx\)
  3.1.26 \(\int \frac {1+\sqrt {3}-x}{(1-\sqrt {3}-x) \sqrt {-1+x^3}} \, dx\)
  3.1.27 \(\int \frac {1+\sqrt {3}+x}{(1-\sqrt {3}+x) \sqrt {-1-x^3}} \, dx\)
  3.1.28 \(\int \frac {(1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\)
  3.1.29 \(\int \frac {(1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\)
  3.1.30 \(\int \frac {(1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\)
  3.1.31 \(\int \frac {(1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\)
  3.1.32 \(\int \frac {1+\sqrt {3}+\sqrt [3]{\frac {b}{a}} x}{(1-\sqrt {3}+\sqrt [3]{\frac {b}{a}} x) \sqrt {a+b x^3}} \, dx\)
  3.1.33 \(\int \frac {1+\sqrt {3}-\sqrt [3]{\frac {b}{a}} x}{(1-\sqrt {3}-\sqrt [3]{\frac {b}{a}} x) \sqrt {a-b x^3}} \, dx\)
  3.1.34 \(\int \frac {1+\sqrt {3}-\sqrt [3]{\frac {b}{a}} x}{(1-\sqrt {3}-\sqrt [3]{\frac {b}{a}} x) \sqrt {-a+b x^3}} \, dx\)
  3.1.35 \(\int \frac {1+\sqrt {3}+\sqrt [3]{\frac {b}{a}} x}{(1-\sqrt {3}+\sqrt [3]{\frac {b}{a}} x) \sqrt {-a-b x^3}} \, dx\)
  3.1.36 \(\int \frac {1-\sqrt {3}+x}{(1+\sqrt {3}+x) \sqrt {1+x^3}} \, dx\)
  3.1.37 \(\int \frac {1-\sqrt {3}-x}{(1+\sqrt {3}-x) \sqrt {1-x^3}} \, dx\)
  3.1.38 \(\int \frac {1-\sqrt {3}-x}{(1+\sqrt {3}-x) \sqrt {-1+x^3}} \, dx\)
  3.1.39 \(\int \frac {1-\sqrt {3}+x}{(1+\sqrt {3}+x) \sqrt {-1-x^3}} \, dx\)
  3.1.40 \(\int \frac {(1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {a+b x^3}} \, dx\)
  3.1.41 \(\int \frac {(1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {a-b x^3}} \, dx\)
  3.1.42 \(\int \frac {(1-\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}-\sqrt [3]{b} x) \sqrt {-a+b x^3}} \, dx\)
  3.1.43 \(\int \frac {(1-\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x}{((1+\sqrt {3}) \sqrt [3]{a}+\sqrt [3]{b} x) \sqrt {-a-b x^3}} \, dx\)
  3.1.44 \(\int \frac {1-\sqrt {3}+\sqrt [3]{\frac {b}{a}} x}{(1+\sqrt {3}+\sqrt [3]{\frac {b}{a}} x) \sqrt {a+b x^3}} \, dx\)
  3.1.45 \(\int \frac {1-\sqrt {3}-\sqrt [3]{\frac {b}{a}} x}{(1+\sqrt {3}-\sqrt [3]{\frac {b}{a}} x) \sqrt {a-b x^3}} \, dx\)
  3.1.46 \(\int \frac {1-\sqrt {3}-\sqrt [3]{\frac {b}{a}} x}{(1+\sqrt {3}-\sqrt [3]{\frac {b}{a}} x) \sqrt {-a+b x^3}} \, dx\)
  3.1.47 \(\int \frac {1-\sqrt {3}+\sqrt [3]{\frac {b}{a}} x}{(1+\sqrt {3}+\sqrt [3]{\frac {b}{a}} x) \sqrt {-a-b x^3}} \, dx\)
  3.1.48 \(\int \frac {c-d x}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\)
  3.1.49 \(\int \frac {e+f x}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\)
  3.1.50 \(\int x^2 (a+b x)^n (c+d x^3) \, dx\)
  3.1.51 \(\int x (a+b x)^n (c+d x^3) \, dx\)
  3.1.52 \(\int (a+b x)^n (c+d x^3) \, dx\)
  3.1.53 \(\int x^2 (a+b x)^n (c+d x^3)^2 \, dx\)
  3.1.54 \(\int x (a+b x)^n (c+d x^3)^2 \, dx\)
  3.1.55 \(\int (a+b x)^n (c+d x^3)^2 \, dx\)
  3.1.56 \(\int x^2 (a+b x)^n (c+d x^3)^3 \, dx\)
  3.1.57 \(\int x (a+b x)^n (c+d x^3)^3 \, dx\)
  3.1.58 \(\int (a+b x)^n (c+d x^3)^3 \, dx\)
  3.1.59 \(\int \frac {2-2 x-x^2}{(2+x^2) \sqrt {1+x^3}} \, dx\)
  3.1.60 \(\int \frac {2+2 x-x^2}{(2+x^2) \sqrt {1-x^3}} \, dx\)
  3.1.61 \(\int \frac {2+2 x-x^2}{(2+x^2) \sqrt {-1+x^3}} \, dx\)
  3.1.62 \(\int \frac {2-2 x-x^2}{(2+x^2) \sqrt {-1-x^3}} \, dx\)
  3.1.63 \(\int \frac {2-2 x-x^2}{(2+d+d x+x^2) \sqrt {1+x^3}} \, dx\)
  3.1.64 \(\int \frac {2+2 x-x^2}{(2-d+d x+x^2) \sqrt {1-x^3}} \, dx\)
  3.1.65 \(\int \frac {2+2 x-x^2}{(2-d+d x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.1.66 \(\int \frac {2-2 x-x^2}{(2+d+d x+x^2) \sqrt {-1-x^3}} \, dx\)
  3.1.67 \(\int x^m (c (a+b x^2)^2)^{3/2} \, dx\)
  3.1.68 \(\int x^5 (c (a+b x^2)^2)^{3/2} \, dx\)
  3.1.69 \(\int x^4 (c (a+b x^2)^2)^{3/2} \, dx\)
  3.1.70 \(\int x^3 (c (a+b x^2)^2)^{3/2} \, dx\)
  3.1.71 \(\int x^2 (c (a+b x^2)^2)^{3/2} \, dx\)
  3.1.72 \(\int x (c (a+b x^2)^2)^{3/2} \, dx\)
  3.1.73 \(\int (c (a+b x^2)^2)^{3/2} \, dx\)
  3.1.74 \(\int \frac {(c (a+b x^2)^2)^{3/2}}{x} \, dx\)
  3.1.75 \(\int \frac {(c (a+b x^2)^2)^{3/2}}{x^2} \, dx\)
  3.1.76 \(\int \frac {(c (a+b x^2)^2)^{3/2}}{x^3} \, dx\)
  3.1.77 \(\int x^2 (c (a+b x^2)^3)^{3/2} \, dx\)
  3.1.78 \(\int x (c (a+b x^2)^3)^{3/2} \, dx\)
  3.1.79 \(\int (c (a+b x^2)^3)^{3/2} \, dx\)
  3.1.80 \(\int \frac {(c (a+b x^2)^3)^{3/2}}{x} \, dx\)
  3.1.81 \(\int \frac {(c (a+b x^2)^3)^{3/2}}{x^2} \, dx\)
  3.1.82 \(\int \frac {(c (a+b x^2)^3)^{3/2}}{x^3} \, dx\)
  3.1.83 \(\int x^2 (\frac {c}{a+b x^2})^{3/2} \, dx\)
  3.1.84 \(\int x (\frac {c}{a+b x^2})^{3/2} \, dx\)
  3.1.85 \(\int (\frac {c}{a+b x^2})^{3/2} \, dx\)
  3.1.86 \(\int \frac {(\frac {c}{a+b x^2})^{3/2}}{x} \, dx\)
  3.1.87 \(\int \frac {(\frac {c}{a+b x^2})^{3/2}}{x^2} \, dx\)
  3.1.88 \(\int \frac {(\frac {c}{a+b x^2})^{3/2}}{x^3} \, dx\)
  3.1.89 \(\int x^7 (c \sqrt {a+b x^2})^{3/2} \, dx\)
  3.1.90 \(\int x^5 (c \sqrt {a+b x^2})^{3/2} \, dx\)
  3.1.91 \(\int x^3 (c \sqrt {a+b x^2})^{3/2} \, dx\)
  3.1.92 \(\int x (c \sqrt {a+b x^2})^{3/2} \, dx\)
  3.1.93 \(\int \frac {(c \sqrt {a+b x^2})^{3/2}}{x} \, dx\)
  3.1.94 \(\int \frac {(c \sqrt {a+b x^2})^{3/2}}{x^3} \, dx\)
  3.1.95 \(\int \sqrt {(b-x) (-a+x)} \, dx\)
  3.1.96 \(\int \frac {1}{\sqrt {(b-x) (-a+x)}} \, dx\)
  3.1.97 \(\int x^5 \sqrt {\frac {e (a+b x^2)}{c+d x^2}} \, dx\)
  3.1.98 \(\int x^3 \sqrt {\frac {e (a+b x^2)}{c+d x^2}} \, dx\)
  3.1.99 \(\int x \sqrt {\frac {e (a+b x^2)}{c+d x^2}} \, dx\)
  3.1.100 \(\int \frac {\sqrt {\frac {e (a+b x^2)}{c+d x^2}}}{x} \, dx\)