3.1.1 \(\int \genfrac {}{}{}{}{1}{\sqrt {1-a x}} \, dx\) [1]
3.1.2 \(\int \genfrac {}{}{}{}{-2 \log (-\sqrt {-1+a x})+\log (-1+a x)}{2 \pi \sqrt {-1+a x}} \, dx\) [2]
3.1.3 \(\int \genfrac {}{}{}{}{1}{(2 x+\sqrt {1+x^2})^2} \, dx\) [3]
3.1.4 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+x^2} (-4+3 x^2)^2} \, dx\) [4]
3.1.5 \(\int \genfrac {}{}{}{}{1}{(2 \sqrt {x}+\sqrt {1+x})^2} \, dx\) [5]
3.1.6 \(\int \genfrac {}{}{}{}{\sqrt {-1+x^2}}{(-i+x)^2} \, dx\) [6]
3.1.7 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+x^2} (1+x^2)^2} \, dx\) [7]
3.1.8 \(\int \genfrac {}{}{}{}{1}{(\sqrt {-1+x}+\sqrt {x})^2 \sqrt {-1+x}} \, dx\) [8]
3.1.9 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+x^2} (\sqrt {x}+\sqrt {-1+x^2})^2} \, dx\) [9]
3.1.10 \(\int \genfrac {}{}{}{}{(\sqrt {x}-\sqrt {-1+x^2})^2}{(1+x-x^2)^2 \sqrt {-1+x^2}} \, dx\) [10]
3.1.11 \(\int (\genfrac {}{}{}{}{1}{\sqrt {2} (1+x)^2 \sqrt {-i+x^2}}+\genfrac {}{}{}{}{1}{\sqrt {2} (1+x)^2 \sqrt {i+x^2}}) \, dx\) [11]
3.1.12 \(\int \genfrac {}{}{}{}{\sqrt {x^2+\sqrt {1+x^4}}}{(1+x)^2 \sqrt {1+x^4}} \, dx\) [12]
3.1.13 \(\int \genfrac {}{}{}{}{\sqrt {x^2+\sqrt {1+x^4}}}{(1+x) \sqrt {1+x^4}} \, dx\) [13]
3.1.14 \(\int \genfrac {}{}{}{}{\sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\) [14]
3.1.15 \(\int \genfrac {}{}{}{}{\sqrt {-x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\) [15]
3.1.16 \(\int \genfrac {}{}{}{}{(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx\) [16]
3.1.17 \(\int (x+\sqrt {a+x^2})^b \, dx\) [17]
3.1.18 \(\int (x-\sqrt {a+x^2})^b \, dx\) [18]
3.1.19 \(\int \genfrac {}{}{}{}{(x+\sqrt {a+x^2})^b}{\sqrt {a+x^2}} \, dx\) [19]
3.1.20 \(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^b}{\sqrt {a+x^2}} \, dx\) [20]
3.1.21 \(\int \genfrac {}{}{}{}{1}{(a+b e^{p x})^2} \, dx\) [21]
3.1.22 \(\int \genfrac {}{}{}{}{1}{(b e^{-p x}+a e^{p x})^2} \, dx\) [22]
3.1.23 \(\int \genfrac {}{}{}{}{x}{(b e^{-p x}+a e^{p x})^2} \, dx\) [23]
3.1.24 \(\int \genfrac {}{}{}{}{1-x+3 x^2}{\sqrt {1-x+x^2} (1+x+x^2)^2} \, dx\) [24]
3.1.25 \(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {a^2+x^2}}}{\sqrt {a^2+x^2}} \, dx\) [25]
3.1.26 \(\int \genfrac {}{}{}{}{\sqrt {b x+\sqrt {a+b^2 x^2}}}{\sqrt {a+b^2 x^2}} \, dx\) [26]
3.1.27 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a^2+x^2} \sqrt {x+\sqrt {a^2+x^2}}} \, dx\) [27]
3.1.28 \(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {a^2+x^2}}}{x} \, dx\) [28]
3.1.29 \(\int x^3 \log ^3(2+x) \log (3+x) \, dx\) [29]
3.1.30 \(\int \genfrac {}{}{}{}{(x+\sqrt {b+x^2})^a}{\sqrt {b+x^2}} \, dx\) [30]
3.1.31 \(\int (x+\sqrt {b+x^2})^a \, dx\) [31]
3.1.32 \(\int (6+3 x^a+2 x^{2 a})^{\genfrac {}{}{}{}{1}{a}} (x^a+x^{2 a}+x^{3 a}) \, dx\) [32]
3.1.33 \(\int \genfrac {}{}{}{}{1}{x \sqrt [3]{1-x^2}} \, dx\) [33]
3.1.34 \(\int \genfrac {}{}{}{}{1}{x (1-x^2)^{2/3}} \, dx\) [34]
3.1.35 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{1-x^3}} \, dx\) [35]
3.1.36 \(\int \genfrac {}{}{}{}{1}{x \sqrt [3]{1-x^3}} \, dx\) [36]
3.1.37 \(\int \genfrac {}{}{}{}{1}{(1+x) \sqrt [3]{1-x^3}} \, dx\) [37]
3.1.38 \(\int \genfrac {}{}{}{}{x}{(1+x) \sqrt [3]{1-x^3}} \, dx\) [38]
3.1.39 \(\int \genfrac {}{}{}{}{1}{x \sqrt [3]{2-3 x+x^2}} \, dx\) [39]
3.1.40 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{-5+7 x-3 x^2+x^3}} \, dx\) [40]
3.1.41 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{x (-q+x^2)}} \, dx\) [41]
3.1.42 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{(-1+x) (q-2 x+x^2)}} \, dx\) [42]
3.1.43 \(\int \genfrac {}{}{}{}{1}{x \sqrt [3]{(-1+x) (q-2 q x+x^2)}} \, dx\) [43]
3.1.44 \(\int \genfrac {}{}{}{}{2-(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx\) [44]
3.1.45 \(\int \genfrac {}{}{}{}{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx\) [45]
3.1.46 \(\int \genfrac {}{}{}{}{a+b x+c x^2}{(1-x+x^2) \sqrt [3]{1-x^3}} \, dx\) [46]
3.1.47 \(\int \genfrac {}{}{}{}{1}{(3-2 x)^{11/2} (1+x+2 x^2)^5} \, dx\) [47]
3.1.48 \(\int \genfrac {}{}{}{}{1}{(3-2 x)^{21/2} (1+x+2 x^2)^{10}} \, dx\) [48]
3.1.49 \(\int \genfrac {}{}{}{}{1}{(3-2 x)^{41/2} (1+x+2 x^2)^{20}} \, dx\) [49]
3.1.50 \(\int \genfrac {}{}{}{}{1}{(3-2 x+x^2)^{11/2} (1+x+2 x^2)^5} \, dx\) [50]
3.1.51 \(\int \genfrac {}{}{}{}{1}{(3-2 x+x^2)^{21/2} (1+x+2 x^2)^{10}} \, dx\) [51]
3.1.52 \(\int \genfrac {}{}{}{}{-a-\sqrt {1+a^2}+x}{(-a+\sqrt {1+a^2}+x) \sqrt {(-a+x) (1+x^2)}} \, dx\) [52]
3.1.53 \(\int \genfrac {}{}{}{}{a+b x}{\sqrt [3]{1-x^2} (3+x^2)} \, dx\) [53]
3.1.54 \(\int \genfrac {}{}{}{}{a+b x}{(3-x^2) \sqrt [3]{1+x^2}} \, dx\) [54]
3.1.55 \(\int \genfrac {}{}{}{}{1}{x \sqrt [3]{4-6 x+3 x^2}} \, dx\) [55]
3.1.56 \(\int x \sqrt [3]{1-x^3} \, dx\) [56]
3.1.57 \(\int \genfrac {}{}{}{}{\sqrt [3]{1-x^3}}{x} \, dx\) [57]
3.1.58 \(\int \genfrac {}{}{}{}{\sqrt [3]{1-x^3}}{1+x} \, dx\) [58]
3.1.59 \(\int \genfrac {}{}{}{}{\sqrt [3]{1-x^3}}{1-x+x^2} \, dx\) [59]
3.1.60 \(\int \genfrac {}{}{}{}{\sqrt [3]{1-x^3}}{2+x} \, dx\) [60]
3.1.61 \(\int \genfrac {}{}{}{}{2+x}{(1+x+x^2) \sqrt [3]{2+x^3}} \, dx\) [61]
3.1.62 \(\int \genfrac {}{}{}{}{3-3 x+30 x^2+160 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx\) [62]
3.1.63 \(\int \genfrac {}{}{}{}{3+12 x+20 x^2}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx\) [63]
3.1.64 \(\int \genfrac {}{}{}{}{-84-576 x-400 x^2+2560 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx\) [64]
3.1.65 \(\int \genfrac {}{}{}{}{\sqrt {1-x^4}}{1+x^4} \, dx\) [65]
3.1.66 \(\int \genfrac {}{}{}{}{\sqrt {1+x^4}}{1-x^4} \, dx\) [66]
3.1.67 \(\int \genfrac {}{}{}{}{\sqrt {1+p x^2+x^4}}{1-x^4} \, dx\) [67]
3.1.68 \(\int \genfrac {}{}{}{}{\sqrt {1+p x^2-x^4}}{1+x^4} \, dx\) [68]
3.1.69 \(\int \genfrac {}{}{}{}{a+b x}{(2-x^2) \sqrt [4]{-1+x^2}} \, dx\) [69]
3.1.70 \(\int \genfrac {}{}{}{}{a+b x}{\sqrt [4]{-1-x^2} (2+x^2)} \, dx\) [70]
3.1.71 \(\int \genfrac {}{}{}{}{a+b x}{\sqrt [4]{1-x^2} (2-x^2)} \, dx\) [71]
3.1.72 \(\int \genfrac {}{}{}{}{a+b x}{\sqrt [4]{1+x^2} (2+x^2)} \, dx\) [72]
3.1.73 \(\int \genfrac {}{}{}{}{x}{\sqrt {1-x^3} (4-x^3)} \, dx\) [73]
3.1.74 \(\int \genfrac {}{}{}{}{x}{(4-d x^3) \sqrt {-1+d x^3}} \, dx\) [74]
3.1.75 \(\int \genfrac {}{}{}{}{x}{\sqrt {-1+x^3} (8+x^3)} \, dx\) [75]
3.1.76 \(\int \genfrac {}{}{}{}{x}{(8-d x^3) \sqrt {1+d x^3}} \, dx\) [76]
3.1.77 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{1-3 x^2} (3-x^2)} \, dx\) [77]
3.1.78 \(\int \genfrac {}{}{}{}{1}{(3+x^2) \sqrt [3]{1+3 x^2}} \, dx\) [78]
3.1.79 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{1-x^2} (3+x^2)} \, dx\) [79]
3.1.80 \(\int \genfrac {}{}{}{}{1}{(3-x^2) \sqrt [3]{1+x^2}} \, dx\) [80]
3.1.81 \(\int \genfrac {}{}{}{}{a+x}{(-a+x) \sqrt {a^2 x-(1+a^2) x^2+x^3}} \, dx\) [81]
3.1.82 \(\int \genfrac {}{}{}{}{-2+a+x}{(-a+x) \sqrt {(2-a) a x+(-1-2 a+a^2) x^2+x^3}} \, dx\) [82]
3.1.83 \(\int \genfrac {}{}{}{}{-a+(-1+2 a) x}{(-a+x) \sqrt {a^2 x-(-1+2 a+a^2) x^2+(-1+2 a) x^3}} \, dx\) [83]
3.1.84 \(\int \genfrac {}{}{}{}{1-\sqrt [3]{2} x}{(2^{2/3}+x) \sqrt {1+x^3}} \, dx\) [84]
3.1.85 \(\int \genfrac {}{}{}{}{1+x}{(-2+x) \sqrt {1+x^3}} \, dx\) [85]
3.1.86 \(\int \genfrac {}{}{}{}{x}{\sqrt {1+x^3} (10+6 \sqrt {3}+x^3)} \, dx\) [86]
3.1.87 \(\int \genfrac {}{}{}{}{x}{\sqrt {1+x^3} (10-6 \sqrt {3}+x^3)} \, dx\) [87]
3.1.88 \(\int \genfrac {}{}{}{}{x}{\sqrt {-1+x^3} (-10-6 \sqrt {3}+x^3)} \, dx\) [88]
3.1.89 \(\int \genfrac {}{}{}{}{x}{\sqrt {-1+x^3} (-10+6 \sqrt {3}+x^3)} \, dx\) [89]
3.1.90 \(\int \genfrac {}{}{}{}{1-\sqrt {3}+x}{(1+\sqrt {3}+x) \sqrt {-4+4 \sqrt {3} x^2+x^4}} \, dx\) [90]
3.1.91 \(\int \genfrac {}{}{}{}{1+\sqrt {3}+x}{(1-\sqrt {3}+x) \sqrt {-4-4 \sqrt {3} x^2+x^4}} \, dx\) [91]
3.1.92 \(\int \genfrac {}{}{}{}{-1+x}{(1+x) \sqrt [3]{2+x^3}} \, dx\) [92]
3.1.93 \(\int \genfrac {}{}{}{}{1}{(1+x) \sqrt [3]{2+x^3}} \, dx\) [93]
3.1.94 \(\int \genfrac {}{}{}{}{1}{(1-x^3) \sqrt [3]{a+b x^3}} \, dx\) [94]
3.1.95 \(\int \genfrac {}{}{}{}{1+x}{(1+x+x^2) \sqrt [3]{a+b x^3}} \, dx\) [95]
3.1.96 \(\int \genfrac {}{}{}{}{x^2}{(1-x^3) \sqrt [3]{a+b x^3}} \, dx\) [96]
3.1.97 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{1-x^3} (1+x^3)} \, dx\) [97]
3.1.98 \(\int \genfrac {}{}{}{}{x}{\sqrt [3]{1-x^3} (1+x^3)} \, dx\) [98]
3.1.99 \(\int \genfrac {}{}{}{}{x^2}{\sqrt [3]{1-x^3} (1+x^3)} \, dx\) [99]
3.1.100 \(\int \genfrac {}{}{}{}{1+x}{(1-x+x^2) \sqrt [3]{1-x^3}} \, dx\) [100]