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