3.7.1 \(\int \genfrac {}{}{}{}{(c+d x)^{3/2}}{\sqrt {a+\genfrac {}{}{}{}{b}{x^2}}} \, dx\) [601]
3.7.2 \(\int \genfrac {}{}{}{}{-1+x^3}{(-4 x+x^4)^{2/3}} \, dx\) [602]
3.7.3 \(\int (2-x^2) \sqrt [4]{6 x-x^3} \, dx\) [603]
3.7.4 \(\int (1+x^4) \sqrt {5 x+x^5} \, dx\) [604]
3.7.5 \(\int (2+5 x^4) \sqrt {2 x+x^5} \, dx\) [605]
3.7.6 \(\int \genfrac {}{}{}{}{x+3 x^2}{\sqrt {x^2+2 x^3}} \, dx\) [606]
3.7.7 \(\int \genfrac {}{}{}{}{2+\sqrt [3]{1-5 x}}{3+\sqrt [3]{1-5 x}} \, dx\) [607]
3.7.8 \(\int \genfrac {}{}{}{}{1+\sqrt {x}}{-1+\sqrt {x}} \, dx\) [608]
3.7.9 \(\int \genfrac {}{}{}{}{1-\sqrt {2+3 x}}{1+\sqrt {2+3 x}} \, dx\) [609]
3.7.10 \(\int \genfrac {}{}{}{}{-1+\sqrt {a+b x}}{1+\sqrt {a+b x}} \, dx\) [610]
3.7.11 \(\int \genfrac {}{}{}{}{a+b n x^{-1+n}}{a x+b x^n} \, dx\) [611]
3.7.12 \(\int \genfrac {}{}{}{}{x^{-n} (a+b n x^{-1+n})}{b+a x^{1-n}} \, dx\) [612]
3.7.13 \(\int x (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (2 a d+(3 b d+3 a e+b d m+a e n) x+(4 c d+4 b e+4 a f+2 c d m+b e m+b e n+2 a f n) x^2+(5 c e+5 b f+5 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(6 c f+6 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (7+2 m+3 n) x^5) \, dx\) [613]
3.7.14 \(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (a d+(2 b d+2 a e+b d m+a e n) x+(3 c d+3 b e+3 a f+2 c d m+b e m+b e n+2 a f n) x^2+(4 c e+4 b f+4 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(5 c f+5 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (6+2 m+3 n) x^5) \, dx\) [614]
3.7.15 \(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4) \, dx\) [615]
3.7.16 \(\int \genfrac {}{}{}{}{(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5)}{x^2} \, dx\) [616]
3.7.17 \(\int \genfrac {}{}{}{}{(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5)}{x^3} \, dx\) [617]
3.7.18 \(\int x^3 (a+b \sqrt {c+d x})^2 \, dx\) [618]
3.7.19 \(\int x^2 (a+b \sqrt {c+d x})^2 \, dx\) [619]
3.7.20 \(\int x (a+b \sqrt {c+d x})^2 \, dx\) [620]
3.7.21 \(\int (a+b \sqrt {c+d x})^2 \, dx\) [621]
3.7.22 \(\int \genfrac {}{}{}{}{(a+b \sqrt {c+d x})^2}{x} \, dx\) [622]
3.7.23 \(\int \genfrac {}{}{}{}{(a+b \sqrt {c+d x})^2}{x^2} \, dx\) [623]
3.7.24 \(\int \genfrac {}{}{}{}{(a+b \sqrt {c+d x})^2}{x^3} \, dx\) [624]
3.7.25 \(\int x^3 \sqrt {a+b \sqrt {c+d x}} \, dx\) [625]
3.7.26 \(\int x^2 \sqrt {a+b \sqrt {c+d x}} \, dx\) [626]
3.7.27 \(\int x \sqrt {a+b \sqrt {c+d x}} \, dx\) [627]
3.7.28 \(\int \sqrt {a+b \sqrt {c+d x}} \, dx\) [628]
3.7.29 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {c+d x}}}{x} \, dx\) [629]
3.7.30 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {c+d x}}}{x^2} \, dx\) [630]
3.7.31 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {c+d x}}}{x^3} \, dx\) [631]
3.7.32 \(\int \genfrac {}{}{}{}{x^3}{a+b \sqrt {c+d x}} \, dx\) [632]
3.7.33 \(\int \genfrac {}{}{}{}{x^2}{a+b \sqrt {c+d x}} \, dx\) [633]
3.7.34 \(\int \genfrac {}{}{}{}{x}{a+b \sqrt {c+d x}} \, dx\) [634]
3.7.35 \(\int \genfrac {}{}{}{}{1}{a+b \sqrt {c+d x}} \, dx\) [635]
3.7.36 \(\int \genfrac {}{}{}{}{1}{x (a+b \sqrt {c+d x})} \, dx\) [636]
3.7.37 \(\int \genfrac {}{}{}{}{1}{x^2 (a+b \sqrt {c+d x})} \, dx\) [637]
3.7.38 \(\int \genfrac {}{}{}{}{1}{x^3 (a+b \sqrt {c+d x})} \, dx\) [638]
3.7.39 \(\int \genfrac {}{}{}{}{x^3}{(a+b \sqrt {c+d x})^2} \, dx\) [639]
3.7.40 \(\int \genfrac {}{}{}{}{x^2}{(a+b \sqrt {c+d x})^2} \, dx\) [640]
3.7.41 \(\int \genfrac {}{}{}{}{x}{(a+b \sqrt {c+d x})^2} \, dx\) [641]
3.7.42 \(\int \genfrac {}{}{}{}{1}{(a+b \sqrt {c+d x})^2} \, dx\) [642]
3.7.43 \(\int \genfrac {}{}{}{}{1}{x (a+b \sqrt {c+d x})^2} \, dx\) [643]
3.7.44 \(\int \genfrac {}{}{}{}{1}{x^2 (a+b \sqrt {c+d x})^2} \, dx\) [644]
3.7.45 \(\int \genfrac {}{}{}{}{1}{x^3 (a+b \sqrt {c+d x})^2} \, dx\) [645]
3.7.46 \(\int \genfrac {}{}{}{}{x^3}{\sqrt {a+b \sqrt {c+d x}}} \, dx\) [646]
3.7.47 \(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b \sqrt {c+d x}}} \, dx\) [647]
3.7.48 \(\int \genfrac {}{}{}{}{x}{\sqrt {a+b \sqrt {c+d x}}} \, dx\) [648]
3.7.49 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {c+d x}}} \, dx\) [649]
3.7.50 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b \sqrt {c+d x}}} \, dx\) [650]
3.7.51 \(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {a+b \sqrt {c+d x}}} \, dx\) [651]
3.7.52 \(\int \genfrac {}{}{}{}{1}{x^3 \sqrt {a+b \sqrt {c+d x}}} \, dx\) [652]
3.7.53 \(\int x^3 (a+b \sqrt {c+d x})^p \, dx\) [653]
3.7.54 \(\int x^2 (a+b \sqrt {c+d x})^p \, dx\) [654]
3.7.55 \(\int x (a+b \sqrt {c+d x})^p \, dx\) [655]
3.7.56 \(\int (a+b \sqrt {c+d x})^p \, dx\) [656]
3.7.57 \(\int \genfrac {}{}{}{}{(a+b \sqrt {c+d x})^p}{x} \, dx\) [657]
3.7.58 \(\int \genfrac {}{}{}{}{(a+b (c x)^n)^{5/2}}{x} \, dx\) [658]
3.7.59 \(\int \genfrac {}{}{}{}{(a+b (c x)^n)^{3/2}}{x} \, dx\) [659]
3.7.60 \(\int \genfrac {}{}{}{}{\sqrt {a+b (c x)^n}}{x} \, dx\) [660]
3.7.61 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c x)^n}} \, dx\) [661]
3.7.62 \(\int \genfrac {}{}{}{}{1}{x (a+b (c x)^n)^{3/2}} \, dx\) [662]
3.7.63 \(\int \genfrac {}{}{}{}{1}{x (a+b (c x)^n)^{5/2}} \, dx\) [663]
3.7.64 \(\int \genfrac {}{}{}{}{(-a+b (c x)^n)^{5/2}}{x} \, dx\) [664]
3.7.65 \(\int \genfrac {}{}{}{}{(-a+b (c x)^n)^{3/2}}{x} \, dx\) [665]
3.7.66 \(\int \genfrac {}{}{}{}{\sqrt {-a+b (c x)^n}}{x} \, dx\) [666]
3.7.67 \(\int \genfrac {}{}{}{}{1}{x \sqrt {-a+b (c x)^n}} \, dx\) [667]
3.7.68 \(\int \genfrac {}{}{}{}{1}{x (-a+b (c x)^n)^{3/2}} \, dx\) [668]
3.7.69 \(\int \genfrac {}{}{}{}{1}{x (-a+b (c x)^n)^{5/2}} \, dx\) [669]
3.7.70 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b x}} \, dx\) [670]
3.7.71 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c x)^m}} \, dx\) [671]
3.7.72 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c (d x)^m)^n}} \, dx\) [672]
3.7.73 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c (d (e x)^m)^n)^p}} \, dx\) [673]
3.7.74 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a+b (c (d (e (f x)^m)^n)^p)^q}} \, dx\) [674]
3.7.75 \(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}} (-1+x^2)^3}{x} \, dx\) [675]
3.7.76 \(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}} (-1+x^2)^2}{x} \, dx\) [676]
3.7.77 \(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}} (-1+x^2)}{x} \, dx\) [677]
3.7.78 \(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}}}{x (-1+x^2)} \, dx\) [678]
3.7.79 \(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}}}{x (-1+x^2)^2} \, dx\) [679]
3.7.80 \(\int \genfrac {}{}{}{}{\sqrt {-1+\genfrac {}{}{}{}{1}{x^2}}}{x (-1+x^2)^3} \, dx\) [680]
3.7.81 \(\int \genfrac {}{}{}{}{\sqrt {1+\genfrac {}{}{}{}{1}{x^2}} x}{(1+x^2)^2} \, dx\) [681]
3.7.82 \(\int \genfrac {}{}{}{}{1}{\sqrt {1+\genfrac {}{}{}{}{1}{x^2}} x (1+x^2)} \, dx\) [682]
3.7.83 \(\int \genfrac {}{}{}{}{x}{a+b x^2+\sqrt {a+b x^2}} \, dx\) [683]
3.7.84 \(\int \genfrac {}{}{}{}{x}{x^2-\sqrt [3]{x^2}} \, dx\) [684]
3.7.85 \(\int x (1+x^2)^3 \sqrt {2+2 x^2+x^4} \, dx\) [685]
3.7.86 \(\int x^5 \sqrt {1-x^3} (1+x^9)^2 \, dx\) [686]
3.7.87 \(\int (\genfrac {}{}{}{}{x}{(a+b x^2)^{3/2}}+\genfrac {}{}{}{}{x}{(1+x^2) \sqrt {a+b x^2}}) \, dx\) [687]
3.7.88 \(\int \genfrac {}{}{}{}{x (1+a+x^2+b x^2)}{(1+x^2) (a+b x^2)^{3/2}} \, dx\) [688]
3.7.89 \(\int (\genfrac {}{}{}{}{x}{(a+b x^2)^{5/2}}+\genfrac {}{}{}{}{x}{(a+b x^2)^{3/2}}+\genfrac {}{}{}{}{x}{(1+x^2) \sqrt {a+b x^2}}) \, dx\) [689]
3.7.90 \(\int \genfrac {}{}{}{}{x (1+a+a^2+x^2+a x^2+b x^2+2 a b x^2+b x^4+b^2 x^4)}{(1+x^2) (a+b x^2)^{5/2}} \, dx\) [690]
3.7.91 \(\int \genfrac {}{}{}{}{1}{\sqrt {\sqrt {x}+x}} \, dx\) [691]
3.7.92 \(\int \sqrt {\sqrt {x}+x} \, dx\) [692]
3.7.93 \(\int \sqrt {-x} (\sqrt {-x}+x) \, dx\) [693]
3.7.94 \(\int \genfrac {}{}{}{}{5+\sqrt [4]{x}}{-6+x} \, dx\) [694]
3.7.95 \(\int \genfrac {}{}{}{}{1}{4+\sqrt {4-x}-x} \, dx\) [695]
3.7.96 \(\int \genfrac {}{}{}{}{1}{1+x-\sqrt {2+x}} \, dx\) [696]
3.7.97 \(\int \genfrac {}{}{}{}{1}{4+x+\sqrt {1+x}} \, dx\) [697]
3.7.98 \(\int \genfrac {}{}{}{}{1}{x-\sqrt {1+x}} \, dx\) [698]
3.7.99 \(\int \genfrac {}{}{}{}{1}{x-\sqrt {2+x}} \, dx\) [699]
3.7.100 \(\int \genfrac {}{}{}{}{1}{-\sqrt {1-x}+x} \, dx\) [700]