3.22.1 \(\int (a+b x) (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\) [2101]
3.22.2 \(\int (a+b x) \sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\) [2102]
3.22.3 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{\sqrt {d+e x}} \, dx\) [2103]
3.22.4 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{3/2}} \, dx\) [2104]
3.22.5 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{5/2}} \, dx\) [2105]
3.22.6 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{7/2}} \, dx\) [2106]
3.22.7 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{9/2}} \, dx\) [2107]
3.22.8 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{11/2}} \, dx\) [2108]
3.22.9 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{13/2}} \, dx\) [2109]
3.22.10 \(\int (a+b x) (d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\) [2110]
3.22.11 \(\int (a+b x) (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\) [2111]
3.22.12 \(\int (a+b x) \sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\) [2112]
3.22.13 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{\sqrt {d+e x}} \, dx\) [2113]
3.22.14 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{3/2}} \, dx\) [2114]
3.22.15 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{5/2}} \, dx\) [2115]
3.22.16 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{7/2}} \, dx\) [2116]
3.22.17 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{9/2}} \, dx\) [2117]
3.22.18 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{11/2}} \, dx\) [2118]
3.22.19 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{13/2}} \, dx\) [2119]
3.22.20 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{15/2}} \, dx\) [2120]
3.22.21 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{17/2}} \, dx\) [2121]
3.22.22 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{7/2}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2122]
3.22.23 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{5/2}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2123]
3.22.24 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{3/2}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2124]
3.22.25 \(\int \genfrac {}{}{}{}{(a+b x) \sqrt {d+e x}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2125]
3.22.26 \(\int \genfrac {}{}{}{}{a+b x}{\sqrt {d+e x} \sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2126]
3.22.27 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{3/2} \sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2127]
3.22.28 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{5/2} \sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2128]
3.22.29 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{7/2} \sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2129]
3.22.30 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{7/2}}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2130]
3.22.31 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{5/2}}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2131]
3.22.32 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{3/2}}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2132]
3.22.33 \(\int \genfrac {}{}{}{}{(a+b x) \sqrt {d+e x}}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2133]
3.22.34 \(\int \genfrac {}{}{}{}{a+b x}{\sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2134]
3.22.35 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2135]
3.22.36 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2136]
3.22.37 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{7/2} (a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2137]
3.22.38 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{7/2}}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2138]
3.22.39 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{5/2}}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2139]
3.22.40 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^{3/2}}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2140]
3.22.41 \(\int \genfrac {}{}{}{}{(a+b x) \sqrt {d+e x}}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2141]
3.22.42 \(\int \genfrac {}{}{}{}{a+b x}{\sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2142]
3.22.43 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2143]
3.22.44 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2144]
3.22.45 \(\int \genfrac {}{}{}{}{a+b x}{(d+e x)^{7/2} (a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2145]
3.22.46 \(\int (a+b x) (d+e x)^m (a^2+2 a b x+b^2 x^2)^3 \, dx\) [2146]
3.22.47 \(\int (a+b x) (d+e x)^m (a^2+2 a b x+b^2 x^2)^2 \, dx\) [2147]
3.22.48 \(\int (a+b x) (d+e x)^m (a^2+2 a b x+b^2 x^2) \, dx\) [2148]
3.22.49 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^m}{a^2+2 a b x+b^2 x^2} \, dx\) [2149]
3.22.50 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^m}{(a^2+2 a b x+b^2 x^2)^2} \, dx\) [2150]
3.22.51 \(\int (a+b x) (d+e x)^m (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\) [2151]
3.22.52 \(\int (a+b x) (d+e x)^m (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\) [2152]
3.22.53 \(\int (a+b x) (d+e x)^m \sqrt {a^2+2 a b x+b^2 x^2} \, dx\) [2153]
3.22.54 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^m}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [2154]
3.22.55 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^m}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2155]
3.22.56 \(\int \genfrac {}{}{}{}{(a+b x) (d+e x)^m}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [2156]
3.22.57 \(\int (a c+b c x) (d+e x)^{-3-2 p} (a^2+2 a b x+b^2 x^2)^p \, dx\) [2157]
3.22.58 \(\int (a+b x) (d+e x)^3 (a^2+2 a b x+b^2 x^2)^p \, dx\) [2158]
3.22.59 \(\int (a+b x) (d+e x)^2 (a^2+2 a b x+b^2 x^2)^p \, dx\) [2159]
3.22.60 \(\int (a+b x) (d+e x) (a^2+2 a b x+b^2 x^2)^p \, dx\) [2160]
3.22.61 \(\int (a+b x) (a^2+2 a b x+b^2 x^2)^p \, dx\) [2161]
3.22.62 \(\int \genfrac {}{}{}{}{(a+b x) (a^2+2 a b x+b^2 x^2)^p}{d+e x} \, dx\) [2162]
3.22.63 \(\int (A+B x) (a c+b c x)^m (a^2+2 a b x+b^2 x^2)^3 \, dx\) [2163]
3.22.64 \(\int \genfrac {}{}{}{}{(A+B x) (a c+b c x)^m}{(a^2+2 a b x+b^2 x^2)^3} \, dx\) [2164]
3.22.65 \(\int (A+B x) (a c+b c x)^m (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\) [2165]
3.22.66 \(\int \genfrac {}{}{}{}{(A+B x) (a c+b c x)^m}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [2166]
3.22.67 \(\int (a c+b c x)^m (f+g x) (a^2+2 a b x+b^2 x^2)^p \, dx\) [2167]
3.22.68 \(\int (a c+b c x)^{-3-2 p} (f+g x) (a^2+2 a b x+b^2 x^2)^p \, dx\) [2168]
3.22.69 \(\int (a+b x) (a c+b c x)^m (a^2+2 a b x+b^2 x^2)^p \, dx\) [2169]
3.22.70 \(\int (a+b x) (a c+b c x)^m (a^2+2 a b x+b^2 x^2)^3 \, dx\) [2170]
3.22.71 \(\int \genfrac {}{}{}{}{(a+b x) (a c+b c x)^m}{(a^2+2 a b x+b^2 x^2)^3} \, dx\) [2171]
3.22.72 \(\int (d+e x)^3 (f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2} \, dx\) [2172]
3.22.73 \(\int (d+e x)^2 (f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2} \, dx\) [2173]
3.22.74 \(\int (d+e x) (f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2} \, dx\) [2174]
3.22.75 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{d+e x} \, dx\) [2175]
3.22.76 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^2} \, dx\) [2176]
3.22.77 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^3} \, dx\) [2177]
3.22.78 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^4} \, dx\) [2178]
3.22.79 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^5} \, dx\) [2179]
3.22.80 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^6} \, dx\) [2180]
3.22.81 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^7} \, dx\) [2181]
3.22.82 \(\int \genfrac {}{}{}{}{(f+g x) \sqrt {c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^8} \, dx\) [2182]
3.22.83 \(\int (d+e x)^3 (f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2} \, dx\) [2183]
3.22.84 \(\int (d+e x)^2 (f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2} \, dx\) [2184]
3.22.85 \(\int (d+e x) (f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2} \, dx\) [2185]
3.22.86 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{d+e x} \, dx\) [2186]
3.22.87 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^2} \, dx\) [2187]
3.22.88 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^3} \, dx\) [2188]
3.22.89 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^4} \, dx\) [2189]
3.22.90 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^5} \, dx\) [2190]
3.22.91 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^6} \, dx\) [2191]
3.22.92 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^7} \, dx\) [2192]
3.22.93 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^8} \, dx\) [2193]
3.22.94 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{3/2}}{(d+e x)^9} \, dx\) [2194]
3.22.95 \(\int (d+e x)^3 (f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2} \, dx\) [2195]
3.22.96 \(\int (d+e x)^2 (f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2} \, dx\) [2196]
3.22.97 \(\int (d+e x) (f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2} \, dx\) [2197]
3.22.98 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2}}{d+e x} \, dx\) [2198]
3.22.99 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2}}{(d+e x)^2} \, dx\) [2199]
3.22.100 \(\int \genfrac {}{}{}{}{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2}}{(d+e x)^3} \, dx\) [2200]