3.22.1 \(\int \genfrac {}{}{}{}{(-1+x^4)^{3/4}}{-1+2 x^4+x^8} \, dx\) [2101]
3.22.2 \(\int \genfrac {}{}{}{}{1+x^4}{(-1+x^4) \sqrt {1+\sqrt {1+x^2}}} \, dx\) [2102]
3.22.3 \(\int \genfrac {}{}{}{}{1}{x^3 (-b+a x^2)^{3/4}} \, dx\) [2103]
3.22.4 \(\int \genfrac {}{}{}{}{a b-2 b x+x^2}{\sqrt [4]{x (-a+x) (-b+x)^3} (b-(1+a d) x+d x^2)} \, dx\) [2104]
3.22.5 \(\int \genfrac {}{}{}{}{1}{x^4 (-b+a x^3)^{3/4}} \, dx\) [2105]
3.22.6 \(\int \genfrac {}{}{}{}{1}{x^4 \sqrt [4]{-b+a x^3}} \, dx\) [2106]
3.22.7 \(\int \genfrac {}{}{}{}{(2+x) (-1-x+x^2) \sqrt [4]{\genfrac {}{}{}{}{1+x-2 x^2}{1+x+4 x^2}}}{2 x (1+2 x+x^2+x^4)} \, dx\) [2107]
3.22.8 \(\int \genfrac {}{}{}{}{1+x^4}{(-1+x^4) \sqrt {1-x-x^2+x^3+x^4}} \, dx\) [2108]
3.22.9 \(\int \genfrac {}{}{}{}{1}{x^5 (-b+a x^4)^{3/4}} \, dx\) [2109]
3.22.10 \(\int \genfrac {}{}{}{}{a b^3-2 (3 a-b) b^2 x+3 (3 a-b) b x^2-4 a x^3+x^4}{\sqrt [4]{x (-a+x) (-b+x)^3} (a^3-(3 a^2+b^3 d) x+3 (a+b^2 d) x^2-(1+3 b d) x^3+d x^4)} \, dx\) [2110]
3.22.11 \(\int \genfrac {}{}{}{}{1}{x^6 (-b+a x^5)^{3/4}} \, dx\) [2111]
3.22.12 \(\int \genfrac {}{}{}{}{1}{x^7 (-b+a x^6)^{3/4}} \, dx\) [2112]
3.22.13 \(\int \genfrac {}{}{}{}{b^6+a^6 x^6}{\sqrt {b^4+a^4 x^4} (-b^6+a^6 x^6)} \, dx\) [2113]
3.22.14 \(\int \genfrac {}{}{}{}{\sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}}}{1+x} \, dx\) [2114]
3.22.15 \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt {1+\sqrt {1+x^2}}}{-1+x^4} \, dx\) [2115]
3.22.16 \(\int \genfrac {}{}{}{}{-b^2+a x^2}{(b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\) [2116]
3.22.17 \(\int \genfrac {}{}{}{}{x}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\) [2117]
3.22.18 \(\int \genfrac {}{}{}{}{-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} (b-b (1+k) x+(-1+b k) x^2)} \, dx\) [2118]
3.22.19 \(\int \genfrac {}{}{}{}{(-b+a x^2) \sqrt {-b x+a x^3}}{x^2 (b+a x^2)} \, dx\) [2119]
3.22.20 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\) [2120]
3.22.21 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\) [2121]
3.22.22 \(\int \genfrac {}{}{}{}{(-3+x^4) (1-x^3+x^4)^{2/3}}{x^3 (1+x^3+x^4)} \, dx\) [2122]
3.22.23 \(\int \genfrac {}{}{}{}{(-4 b+a x^5) (b+a x^5)^{3/4}}{x^4 (2 b+c x^4+2 a x^5)} \, dx\) [2123]
3.22.24 \(\int \genfrac {}{}{}{}{-1+x^6}{\sqrt [3]{x^2+x^4} (1+x^6)} \, dx\) [2124]
3.22.25 \(\int \genfrac {}{}{}{}{\sqrt [4]{2+3 x^4} (4+6 x^4+x^8)}{x^6 (1+x^4) (1+2 x^4)} \, dx\) [2125]
3.22.26 \(\int \genfrac {}{}{}{}{\sqrt [8]{256-256 x^2+96 x^4-16 x^6+x^8}}{-1+x^3} \, dx\) [2126]
3.22.27 \(\int \genfrac {}{}{}{}{-36-6 x^2+6 x^3+x^6}{x (-6+x^3) \sqrt [6]{\genfrac {}{}{}{}{6+x^3}{-6+x^3}} (36-90 x+122 x^2-96 x^3+51 x^4-26 x^5+15 x^6-6 x^7+x^8)} \, dx\) [2127]
3.22.28 \(\int \genfrac {}{}{}{}{2 b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-2 b+a x^4+x^8)} \, dx\) [2128]
3.22.29 \(\int \genfrac {}{}{}{}{2 b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-2 b+a x^4+x^8)} \, dx\) [2129]
3.22.30 \(\int \genfrac {}{}{}{}{-b+a x^8}{(b+a x^8) \sqrt [4]{b-c x^4+a x^8}} \, dx\) [2130]
3.22.31 \(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\) [2131]
3.22.32 \(\int \genfrac {}{}{}{}{1+\sqrt {1+x^2}}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\) [2132]
3.22.33 \(\int \genfrac {}{}{}{}{-2+(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (b-b (1+k) x+(-1+b k) x^2)} \, dx\) [2133]
3.22.34 \(\int \genfrac {}{}{}{}{\sqrt [4]{-b+a x^4} (-8 b+a x^8)}{x^{10} (b+a x^4)} \, dx\) [2134]
3.22.35 \(\int \genfrac {}{}{}{}{x}{x+\sqrt {x+\sqrt {1+x}}} \, dx\) [2135]
3.22.36 \(\int \genfrac {}{}{}{}{x}{x+\sqrt {x+\sqrt {1+x}}} \, dx\) [2136]
3.22.37 \(\int \genfrac {}{}{}{}{(-6+x^2) (-2+x^2) (2-x^2+x^3) \sqrt [3]{-2+x^2+2 x^3}}{x^5 (-2+x^2+x^3)^2} \, dx\) [2137]
3.22.38 \(\int \genfrac {}{}{}{}{(-1+x) \sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\) [2138]
3.22.39 \(\int \genfrac {}{}{}{}{(-1+x) \sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\) [2139]
3.22.40 \(\int \genfrac {}{}{}{}{(1+x) \sqrt [4]{x^3+x^5}}{x (-1+x^3)} \, dx\) [2140]
3.22.41 \(\int \genfrac {}{}{}{}{x^3}{\sqrt [3]{-b x^2+a x^3} (-b^2+a^2 x^6)} \, dx\) [2141]
3.22.42 \(\int \genfrac {}{}{}{}{1+x^2}{(-1+x^2) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2142]
3.22.43 \(\int \genfrac {}{}{}{}{1+x^2}{(-1+x^2) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2143]
3.22.44 \(\int \genfrac {}{}{}{}{-1+x+x^3}{(1-x+x^3) \sqrt [3]{-x^2+x^3}} \, dx\) [2144]
3.22.45 \(\int \genfrac {}{}{}{}{-1+x+x^3}{(1-x+x^3) \sqrt [3]{-x^2+x^3}} \, dx\) [2145]
3.22.46 \(\int \genfrac {}{}{}{}{(1+2 x^3)^{4/3} (1+3 x^3)}{x^8 (1+4 x^3)} \, dx\) [2146]
3.22.47 \(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt [3]{-x^2+x^4}} \, dx\) [2147]
3.22.48 \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4)}{b+a x^4} \, dx\) [2148]
3.22.49 \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4)}{b+a x^4} \, dx\) [2149]
3.22.50 \(\int \genfrac {}{}{}{}{x^3 (-4 a+3 x)}{(x^2 (-a+x))^{2/3} (a-x+d x^4)} \, dx\) [2150]
3.22.51 \(\int \genfrac {}{}{}{}{b+a x^6}{x^6 (b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\) [2151]
3.22.52 \(\int \genfrac {}{}{}{}{-1+x^2}{\sqrt {1+x} (1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\) [2152]
3.22.53 \(\int \genfrac {}{}{}{}{-1+x^2}{\sqrt {1+x} (1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\) [2153]
3.22.54 \(\int x^2 \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\) [2154]
3.22.55 \(\int \genfrac {}{}{}{}{1}{\sqrt {-b+a^2 x^2} \sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [2155]
3.22.56 \(\int \genfrac {}{}{}{}{(2 a-3 b+x) (-a^3+3 a^2 x-3 a x^2+x^3)}{(-b+x) \sqrt [4]{(-a+x) (-b+x)^2} (-a^3-b^2 d+(3 a^2+2 b d) x-(3 a+d) x^2+x^3)} \, dx\) [2156]
3.22.57 \(\int \genfrac {}{}{}{}{(2-x+2 x^2) \sqrt [4]{-x^3+x^4}}{-2-2 x+x^2} \, dx\) [2157]
3.22.58 \(\int \genfrac {}{}{}{}{(2-x+2 x^2) \sqrt [4]{-x^3+x^4}}{-2-2 x+x^2} \, dx\) [2158]
3.22.59 \(\int \genfrac {}{}{}{}{\sqrt {1-3 x^2-2 x^4} (1+2 x^4)}{(-1+x^2+2 x^4) (-1+2 x^2+2 x^4)} \, dx\) [2159]
3.22.60 \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4} (-b+2 a x^4)}{-2 b+a x^4} \, dx\) [2160]
3.22.61 \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4} (-b+2 a x^4)}{-2 b+a x^4} \, dx\) [2161]
3.22.62 \(\int \genfrac {}{}{}{}{x (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} (a-x+d x^4)} \, dx\) [2162]
3.22.63 \(\int \genfrac {}{}{}{}{-b-2 a x^4+2 x^8}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\) [2163]
3.22.64 \(\int \genfrac {}{}{}{}{-b-2 a x^4+2 x^8}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\) [2164]
3.22.65 \(\int \genfrac {}{}{}{}{1}{(-1+x^2) \sqrt [3]{-x^2+x^3}} \, dx\) [2165]
3.22.66 \(\int \genfrac {}{}{}{}{-b^2+a^2 x^4}{\sqrt {-b x+a x^3} (b^2+c x^2+a^2 x^4)} \, dx\) [2166]
3.22.67 \(\int \genfrac {}{}{}{}{(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x (b x^2+a (q+p x^3)^2)} \, dx\) [2167]
3.22.68 \(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x (b x^4+a (q+p x^3)^2)} \, dx\) [2168]
3.22.69 \(\int \genfrac {}{}{}{}{x^2-\sqrt {1+x^2}}{x^2+\sqrt {x+\sqrt {1+x^2}}} \, dx\) [2169]
3.22.70 \(\int \genfrac {}{}{}{}{x^2-\sqrt {1+x^2}}{x^2+\sqrt {x+\sqrt {1+x^2}}} \, dx\) [2170]
3.22.71 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {1-\sqrt {1+\genfrac {}{}{}{}{1}{x^2}}}}}{x} \, dx\) [2171]
3.22.72 \(\int \genfrac {}{}{}{}{-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} (1-(1+k) x+(-b+k) x^2)} \, dx\) [2172]
3.22.73 \(\int \genfrac {}{}{}{}{2-(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx\) [2173]
3.22.74 \(\int \genfrac {}{}{}{}{-2+(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x+(-b+k) x^2)} \, dx\) [2174]
3.22.75 \(\int \genfrac {}{}{}{}{(3+2 x^2) (1+2 x^2+2 x^3)^{2/3}}{x^3 (-1-2 x^2+x^3)} \, dx\) [2175]
3.22.76 \(\int \genfrac {}{}{}{}{-b+c x+a x^2}{(b+a x^2) \sqrt {-b x+a x^3}} \, dx\) [2176]
3.22.77 \(\int \genfrac {}{}{}{}{-4-2 x+2 x^2+x^4}{x (-2+x^2) \sqrt [4]{\genfrac {}{}{}{}{2+x^2}{-2+x^2}} (8-10 x+4 x^2+4 x^3-4 x^4+x^5)} \, dx\) [2177]
3.22.78 \(\int \genfrac {}{}{}{}{\sqrt {1+x} (-1+x^4) \sqrt {1+\sqrt {1+x}}}{1+x^4} \, dx\) [2178]
3.22.79 \(\int \genfrac {}{}{}{}{\sqrt {1+x} (-1+x^4) \sqrt {1+\sqrt {1+x}}}{1+x^4} \, dx\) [2179]
3.22.80 \(\int \genfrac {}{}{}{}{-d+c x}{x^4 \sqrt [3]{-b+a x^3}} \, dx\) [2180]
3.22.81 \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^3+a x^4} (-d+c x^4)}{x^2} \, dx\) [2181]
3.22.82 \(\int \genfrac {}{}{}{}{x^3 (5-4 (1+k) x+3 k x^2)}{((1-x) x (1-k x))^{2/3} (-b+b (1+k) x-b k x^2+x^5)} \, dx\) [2182]
3.22.83 \(\int \genfrac {}{}{}{}{(-8+x^5) (2+x^5) \sqrt [4]{2-3 x^4+x^5}}{x^6 (4-3 x^4+2 x^5)} \, dx\) [2183]
3.22.84 \(\int \genfrac {}{}{}{}{x^2}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2184]
3.22.85 \(\int \genfrac {}{}{}{}{x^2}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2185]
3.22.86 \(\int \genfrac {}{}{}{}{1+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2186]
3.22.87 \(\int \genfrac {}{}{}{}{1+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2187]
3.22.88 \(\int \genfrac {}{}{}{}{1-x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2188]
3.22.89 \(\int \genfrac {}{}{}{}{1-x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2189]
3.22.90 \(\int \genfrac {}{}{}{}{1+x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2190]
3.22.91 \(\int \genfrac {}{}{}{}{1+x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\) [2191]
3.22.92 \(\int \genfrac {}{}{}{}{(-4+x^3) (-2+x^3) (-1+x^3)^{2/3}}{x^6 (-2+x^3+x^6)} \, dx\) [2192]
3.22.93 \(\int \genfrac {}{}{}{}{(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^8} \, dx\) [2193]
3.22.94 \(\int \genfrac {}{}{}{}{(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^8} \, dx\) [2194]
3.22.95 \(\int \genfrac {}{}{}{}{-1+x^8}{\sqrt [4]{x^2+x^6} (1+x^8)} \, dx\) [2195]
3.22.96 \(\int \genfrac {}{}{}{}{-1+x^8}{\sqrt [4]{x^2+x^6} (1+x^8)} \, dx\) [2196]
3.22.97 \(\int \genfrac {}{}{}{}{x^5 (8-7 (1+k) x+6 k x^2)}{((1-x) x (1-k x))^{2/3} (-b+b (1+k) x-b k x^2+x^8)} \, dx\) [2197]
3.22.98 \(\int \genfrac {}{}{}{}{-2 b-a x^4+2 x^8}{\sqrt [4]{-b+a x^4} (-2 b-a x^4+x^8)} \, dx\) [2198]
3.22.99 \(\int \genfrac {}{}{}{}{\sqrt {b+\sqrt {b^2+a x^2}}}{x^4} \, dx\) [2199]
3.22.100 \(\int \genfrac {}{}{}{}{\sqrt {b+\sqrt {b^2+a x^2}}}{x^4 \sqrt {b^2+a x^2}} \, dx\) [2200]