\(\int \sqrt {\genfrac {}{}{}{}{1-x}{1+x}} \, dx\) [1]
\(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{1-x}{1+x}} (1+x)} \, dx\) [2]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{1-x}{1+x}}}{1-x} \, dx\) [3]
\(\int \genfrac {}{}{}{}{\sqrt {x (-1+x^2)}}{-1+x^4} \, dx\) [4]
\(\int \genfrac {}{}{}{}{x}{\sqrt {x (-1+x^2)} (1+x^2)} \, dx\) [5]
\(\int \genfrac {}{}{}{}{a-c x^4}{\sqrt {a+c x^4} (a d+c d x^4)} \, dx\) [6]
\(\int \genfrac {}{}{}{}{a-c x^4}{\sqrt {a+c x^4} (a d+e x^2+c d x^4)} \, dx\) [7]
\(\int \genfrac {}{}{}{}{a-c x^4}{\sqrt {a+b x^2+c x^4} (a d+c d x^4)} \, dx\) [8]
\(\int \genfrac {}{}{}{}{a-c x^4}{\sqrt {a+b x^2+c x^4} (a d+e x^2+c d x^4)} \, dx\) [9]
\(\int \genfrac {}{}{}{}{(a-c x^4) (a+b x^2+c x^4)^{3/2}}{(a d e+(c d^2+a e^2) x^2+c d e x^4)^3} \, dx\) [10]
\(\int \genfrac {}{}{}{}{(a-c x^4) \sqrt {a+b x^2+c x^4}}{(a d e+(c d^2+a e^2) x^2+c d e x^4)^2} \, dx\) [11]
\(\int \genfrac {}{}{}{}{a-c x^4}{\sqrt {a+b x^2+c x^4} (a d e+(c d^2+a e^2) x^2+c d e x^4)} \, dx\) [12]
\(\int \genfrac {}{}{}{}{a-c x^4}{(a+b x^2+c x^4)^{3/2}} \, dx\) [13]
\(\int \genfrac {}{}{}{}{(a-c x^4) (a d e+(c d^2+a e^2) x^2+c d e x^4)}{(a+b x^2+c x^4)^{5/2}} \, dx\) [14]
\(\int \genfrac {}{}{}{}{(a-c x^4) (a d e+(c d^2+a e^2) x^2+c d e x^4)^2}{(a+b x^2+c x^4)^{7/2}} \, dx\) [15]
\(\int \genfrac {}{}{}{}{(a-c x^4) (a+b x^2+c x^4)^{3/2}}{(a e+c d x^2)^3 (d+e x^2)^3} \, dx\) [16]
\(\int \genfrac {}{}{}{}{(a-c x^4) \sqrt {a+b x^2+c x^4}}{(a e+c d x^2)^2 (d+e x^2)^2} \, dx\) [17]
\(\int \genfrac {}{}{}{}{a-c x^4}{(a e+c d x^2) (d+e x^2) \sqrt {a+b x^2+c x^4}} \, dx\) [18]
\(\int \genfrac {}{}{}{}{a-c x^4}{(a+b x^2+c x^4)^{3/2}} \, dx\) [19]
\(\int \genfrac {}{}{}{}{(a e+c d x^2) (d+e x^2) (a-c x^4)}{(a+b x^2+c x^4)^{5/2}} \, dx\) [20]
\(\int \genfrac {}{}{}{}{(a e+c d x^2)^2 (d+e x^2)^2 (a-c x^4)}{(a+b x^2+c x^4)^{7/2}} \, dx\) [21]
\(\int \genfrac {}{}{}{}{e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\) [22]
\(\int \genfrac {}{}{}{}{e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\) [23]
\(\int \genfrac {}{}{}{}{e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\) [24]
\(\int \genfrac {}{}{}{}{e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\) [25]
\(\int \genfrac {}{}{}{}{e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [26]
\(\int \genfrac {}{}{}{}{e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [27]
\(\int \genfrac {}{}{}{}{x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx\) [28]
\(\int \genfrac {}{}{}{}{x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx\) [29]
\(\int \genfrac {}{}{}{}{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx\) [30]
\(\int \genfrac {}{}{}{}{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx\) [31]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx\) [32]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx\) [33]
\(\int \genfrac {}{}{}{}{x (2 e-2 f x^3)}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx\) [34]
\(\int \genfrac {}{}{}{}{x (2 e-2 f x^3)}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx\) [35]
\(\int \genfrac {}{}{}{}{x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx\) [36]
\(\int \genfrac {}{}{}{}{x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx\) [37]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx\) [38]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx\) [39]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [40]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [41]
\(\int \genfrac {}{}{}{}{x^6}{-1+x^2+\sqrt {1-x^2}} \, dx\) [42]
\(\int \genfrac {}{}{}{}{x^4}{-1+x^2+\sqrt {1-x^2}} \, dx\) [43]
\(\int \genfrac {}{}{}{}{x^2}{-1+x^2+\sqrt {1-x^2}} \, dx\) [44]
\(\int \genfrac {}{}{}{}{1}{-1+x^2+\sqrt {1-x^2}} \, dx\) [45]
\(\int \genfrac {}{}{}{}{1}{x^2 (-1+x^2+\sqrt {1-x^2})} \, dx\) [46]
\(\int \genfrac {}{}{}{}{1}{x^4 (-1+x^2+\sqrt {1-x^2})} \, dx\) [47]
\(\int \genfrac {}{}{}{}{x^5}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [48]
\(\int \genfrac {}{}{}{}{x^3}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [49]
\(\int \genfrac {}{}{}{}{x}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [50]
\(\int \genfrac {}{}{}{}{1}{x (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [51]
\(\int \genfrac {}{}{}{}{1}{x^3 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [52]
\(\int \genfrac {}{}{}{}{x^4}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [53]
\(\int \genfrac {}{}{}{}{x^2}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [54]
\(\int \genfrac {}{}{}{}{1}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [55]
\(\int \genfrac {}{}{}{}{1}{x^2 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [56]
\(\int \genfrac {}{}{}{}{1}{x^4 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [57]
\(\int \genfrac {}{}{}{}{x^8}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [58]
\(\int \genfrac {}{}{}{}{x^5}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [59]
\(\int \genfrac {}{}{}{}{x^2}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [60]
\(\int \genfrac {}{}{}{}{1}{x (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [61]
\(\int \genfrac {}{}{}{}{1}{x^4 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [62]
\(\int \genfrac {}{}{}{}{x^3}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [63]
\(\int \genfrac {}{}{}{}{x}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [64]
\(\int \genfrac {}{}{}{}{1}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [65]
\(\int \genfrac {}{}{}{}{1}{x^2 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [66]
\(\int \genfrac {}{}{}{}{1}{x^3 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [67]
\(\int \genfrac {}{}{}{}{1}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [68]
\(\int \genfrac {}{}{}{}{x^m}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [69]
\(\int \genfrac {}{}{}{}{x^{-1+n}}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [70]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x}+4 x^{3/2}} \, dx\) [71]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x}-x^{5/2}} \, dx\) [72]
\(\int \genfrac {}{}{}{}{1}{-\sqrt [4]{x}+\sqrt {x}} \, dx\) [73]
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{x}+\sqrt {x}} \, dx\) [74]
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{x}+\sqrt {x}} \, dx\) [75]
\(\int \genfrac {}{}{}{}{1}{-\sqrt [3]{x}+x^{2/3}} \, dx\) [76]
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\) [77]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\genfrac {}{}{}{}{1}{\sqrt [4]{x}}} \, dx\) [78]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{x+x^2} \, dx\) [79]
\(\int \genfrac {}{}{}{}{x}{4 \sqrt {x}+x} \, dx\) [80]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt [3]{x}+x} \, dx\) [81]
\(\int \genfrac {}{}{}{}{\sqrt [3]{x}}{\sqrt [4]{x}+\sqrt {x}} \, dx\) [82]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\) [83]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{-\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\sqrt {x}} \, dx\) [84]
\(\int \genfrac {}{}{}{}{-1+x^3}{(-4 x+x^4)^{2/3}} \, dx\) [85]
\(\int (2-x^2) \sqrt [4]{6 x-x^3} \, dx\) [86]
\(\int (1+x^4) \sqrt {5 x+x^5} \, dx\) [87]
\(\int (2+5 x^4) \sqrt {2 x+x^5} \, dx\) [88]
\(\int \genfrac {}{}{}{}{x+3 x^2}{\sqrt {x^2+2 x^3}} \, dx\) [89]
\(\int \genfrac {}{}{}{}{2+\sqrt [3]{1-5 x}}{3+\sqrt [3]{1-5 x}} \, dx\) [90]
\(\int \genfrac {}{}{}{}{1+\sqrt {x}}{-1+\sqrt {x}} \, dx\) [91]
\(\int \genfrac {}{}{}{}{1-\sqrt {2+3 x}}{1+\sqrt {2+3 x}} \, dx\) [92]
\(\int \genfrac {}{}{}{}{-1+\sqrt {a+b x}}{1+\sqrt {a+b x}} \, dx\) [93]
\(\int \genfrac {}{}{}{}{a+b n x^{-1+n}}{a x+b x^n} \, dx\) [94]
\(\int \genfrac {}{}{}{}{x^{-n} (a+b n x^{-1+n})}{b+a x^{1-n}} \, dx\) [95]
\(\int x (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (2 a d+(3 b d+3 a e+b d m+a e n) x+(4 c d+4 b e+4 a f+2 c d m+b e m+b e n+2 a f n) x^2+(5 c e+5 b f+5 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(6 c f+6 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (7+2 m+3 n) x^5) \, dx\) [96]
\(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (a d+(2 b d+2 a e+b d m+a e n) x+(3 c d+3 b e+3 a f+2 c d m+b e m+b e n+2 a f n) x^2+(4 c e+4 b f+4 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(5 c f+5 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (6+2 m+3 n) x^5) \, dx\) [97]
\(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4) \, dx\) [98]
\(\int \genfrac {}{}{}{}{(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5)}{x^2} \, dx\) [99]
\(\int \genfrac {}{}{}{}{(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5)}{x^3} \, dx\) [100]