3.24 Integrals 2301 to 2400

   \(\int \genfrac {}{}{}{}{1-x^4+2 x^8}{\sqrt [4]{1+x^4} (-1-2 x^4+x^8)} \, dx\) [2301]
   \(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{(1+x^2) \sqrt {1+x^4}} \, dx\) [2302]
   \(\int \genfrac {}{}{}{}{x}{x+\sqrt {c+\sqrt {b+a x}}} \, dx\) [2303]
   \(\int \genfrac {}{}{}{}{x}{x+\sqrt {c+\sqrt {b+a x}}} \, dx\) [2304]
   \(\int \genfrac {}{}{}{}{1}{(1+x) \sqrt [3]{1-x+x^2}} \, dx\) [2305]
   \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt [4]{-x^3+x^4}}{x^4 (-1+x^4)} \, dx\) [2306]
   \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt [4]{-x^3+x^4}}{x^4 (-1+x^4)} \, dx\) [2307]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{b x+a x^3} (b+a x^4)}{x^4} \, dx\) [2308]
   \(\int \genfrac {}{}{}{}{b^4+a^4 x^4}{\sqrt {-b^2 x+a^2 x^3} (-b^4+a^4 x^4)} \, dx\) [2309]
   \(\int \genfrac {}{}{}{}{1+x}{(-1+x^3) \sqrt [8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx\) [2310]
   \(\int \genfrac {}{}{}{}{1}{x^2 \sqrt [3]{-1-x+5 x^2+2 x^3-10 x^4+2 x^5+7 x^6-5 x^7+x^8}} \, dx\) [2311]
   \(\int \genfrac {}{}{}{}{c x^6 (-4 b+a x^5)}{(b+a x^5)^{3/4} (b^2+2 a b x^5-c^2 x^8+a^2 x^{10})} \, dx\) [2312]
   \(\int \genfrac {}{}{}{}{x^2 \sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\) [2313]
   \(\int \genfrac {}{}{}{}{a+b x^2+a k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^4 x^4)} \, dx\) [2314]
   \(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (a q^2+2 a p q x^3+b x^4+a p^2 x^6)}{x^9} \, dx\) [2315]
   \(\int \genfrac {}{}{}{}{-1+x^3}{(1+x^3) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\) [2316]
   \(\int \genfrac {}{}{}{}{5 x-4 (1+k) x^2+3 k x^3}{\sqrt [3]{(1-x) x (1-k x)} (-1+(1+k) x-k x^2+b x^5)} \, dx\) [2317]
   \(\int \genfrac {}{}{}{}{x^2 (8-7 (1+k) x+6 k x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-1+(1+k) x-k x^2+b x^8)} \, dx\) [2318]
   \(\int \genfrac {}{}{}{}{x (-a b+x^2)}{(x^2 (-a+x) (-b+x))^{2/3} (a b-(a+b+d) x+x^2)} \, dx\) [2319]
   \(\int \genfrac {}{}{}{}{(b+x^3) (c+x^3)}{\sqrt [3]{a+x^3}} \, dx\) [2320]
   \(\int \genfrac {}{}{}{}{1}{(1+x^3) \sqrt [3]{-x^2+x^3}} \, dx\) [2321]
   \(\int \genfrac {}{}{}{}{1}{(1+x^3) \sqrt [3]{-x^2+x^3}} \, dx\) [2322]
   \(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^3 (a q+b x^2+a p x^3)} \, dx\) [2323]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{x^2+x^6} (1+x^8)}{x^4 (-1+x^4)} \, dx\) [2324]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{x^2+x^6} (1+x^8)}{x^4 (-1+x^4)} \, dx\) [2325]
   \(\int \genfrac {}{}{}{}{1}{x \sqrt [3]{2-3 x+x^2}} \, dx\) [2326]
   \(\int \genfrac {}{}{}{}{a b-x^2}{\sqrt [3]{x^2 (-a+x) (-b+x)} (a b-(a+b+d) x+x^2)} \, dx\) [2327]
   \(\int \genfrac {}{}{}{}{(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^2+a (q+p x^3)^2)}{x^5} \, dx\) [2328]
   \(\int \genfrac {}{}{}{}{1+x}{(-1+x) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2329]
   \(\int \genfrac {}{}{}{}{1+x}{(-1+x) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2330]
   \(\int \genfrac {}{}{}{}{1}{d+c x+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [2331]
   \(\int \genfrac {}{}{}{}{1}{d+c x+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [2332]
   \(\int \genfrac {}{}{}{}{-d+c x}{x^7 \sqrt [3]{-b+a x^3}} \, dx\) [2333]
   \(\int \genfrac {}{}{}{}{1+x^2+x^4}{(1-x^4) \sqrt [4]{x^3+x^5}} \, dx\) [2334]
   \(\int \genfrac {}{}{}{}{\sqrt {-1+2 x^4} (-1+2 x^8)}{x^7 (-1+2 x^4+x^8)} \, dx\) [2335]
   \(\int \genfrac {}{}{}{}{\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2336]
   \(\int \genfrac {}{}{}{}{1+x}{(3+x) (1+2 x) \sqrt [3]{1+x^2}} \, dx\) [2337]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-x^2+x^3}}{1+x+x^2} \, dx\) [2338]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-x^2+x^3}}{1+x+x^2} \, dx\) [2339]
   \(\int \genfrac {}{}{}{}{x (5-4 (1+k) x+3 k x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-b+(b+b k) x-b k x^2+x^5)} \, dx\) [2340]
   \(\int \genfrac {}{}{}{}{1+x^4}{(1-x^4) \sqrt [4]{x^3+x^5}} \, dx\) [2341]
   \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (2+x^3+x^6)}{x^6 (-2+x^3)^2} \, dx\) [2342]
   \(\int \genfrac {}{}{}{}{1+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\) [2343]
   \(\int \genfrac {}{}{}{}{1+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\) [2344]
   \(\int \genfrac {}{}{}{}{x^2 (8-7 (1+k) x+6 k x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-b+b (1+k) x-b k x^2+x^8)} \, dx\) [2345]
   \(\int \genfrac {}{}{}{}{1}{(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [2346]
   \(\int \genfrac {}{}{}{}{x (-a+x) (a b+(a-2 b) x)}{(x (-a+x) (-b+x)^2)^{3/4} (b^2 d+(a-2 b d) x+(-1+d) x^2)} \, dx\) [2347]
   \(\int \genfrac {}{}{}{}{(1+x^2) (1-3 x^2+x^4)}{x^2 \sqrt {\genfrac {}{}{}{}{-2+x+2 x^2}{-1+x+x^2}} (1-x-3 x^2+x^3+x^4)} \, dx\) [2348]
   \(\int \genfrac {}{}{}{}{x^3 (5-4 (1+k) x+3 k x^2)}{((1-x) x (1-k x))^{2/3} (-1+(1+k) x-k x^2+b x^5)} \, dx\) [2349]
   \(\int \genfrac {}{}{}{}{(-2+x^4) \sqrt {2+x^4}}{4+3 x^4+x^8} \, dx\) [2350]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-1-x+5 x^2+2 x^3-10 x^4+2 x^5+7 x^6-5 x^7+x^8}}{x^2} \, dx\) [2351]
   \(\int \genfrac {}{}{}{}{(-b+a^2 x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{\sqrt {b+a^2 x^4}} \, dx\) [2352]
   \(\int \genfrac {}{}{}{}{\sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\) [2353]
   \(\int \genfrac {}{}{}{}{\sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\) [2354]
   \(\int \genfrac {}{}{}{}{-i+\sqrt {k} x}{(i+\sqrt {k} x) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\) [2355]
   \(\int \genfrac {}{}{}{}{i+\sqrt {k} x}{(-i+\sqrt {k} x) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\) [2356]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{-1+3 x-3 x^2+x^3} (-1-2 x+x^2+3 x^3)^4} \, dx\) [2357]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\) [2358]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\) [2359]
   \(\int \genfrac {}{}{}{}{x^4}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\) [2360]
   \(\int \genfrac {}{}{}{}{x^4}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\) [2361]
   \(\int \genfrac {}{}{}{}{(-1+x^4) \sqrt [4]{x^2+x^6}}{1-x^4+x^8} \, dx\) [2362]
   \(\int \genfrac {}{}{}{}{(-1+x^4) \sqrt [4]{x^2+x^6}}{1-x^4+x^8} \, dx\) [2363]
   \(\int \genfrac {}{}{}{}{1-x^4+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\) [2364]
   \(\int \genfrac {}{}{}{}{1-x^4+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\) [2365]
   \(\int \genfrac {}{}{}{}{1}{(-b+a x) \sqrt [4]{-x^3+x^4}} \, dx\) [2366]
   \(\int \genfrac {}{}{}{}{-x+x^2}{\sqrt {(1-x) x (1-k^2 x)} (1-2 x+k^2 x^2)} \, dx\) [2367]
   \(\int \genfrac {}{}{}{}{-b+a^3 x^2}{(b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\) [2368]
   \(\int \genfrac {}{}{}{}{-b+a^3 x^2}{(b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\) [2369]
   \(\int \genfrac {}{}{}{}{1+x^2}{(-1+x^2) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\) [2370]
   \(\int \genfrac {}{}{}{}{x^4 \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\) [2371]
   \(\int \genfrac {}{}{}{}{x^4 \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\) [2372]
   \(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q+p x^3}}{c x^4+b x^2 (q+p x^3)+a (q+p x^3)^2} \, dx\) [2373]
   \(\int \genfrac {}{}{}{}{(-1+x^4)^2}{(1+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\) [2374]
   \(\int \genfrac {}{}{}{}{\sqrt {x^2+\sqrt {1+x^4}}}{(1+x^2)^2 \sqrt {1+x^4}} \, dx\) [2375]
   \(\int \genfrac {}{}{}{}{\sqrt {q+p x^5} (-2 q+3 p x^5)}{c x^4+b x^2 (q+p x^5)+a (q+p x^5)^2} \, dx\) [2376]
   \(\int \genfrac {}{}{}{}{1}{x \sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [2377]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{1+x^2} (9+x^2)} \, dx\) [2378]
   \(\int \genfrac {}{}{}{}{b+a^3 x^2}{(-b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\) [2379]
   \(\int \genfrac {}{}{}{}{b+a^3 x^2}{(-b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\) [2380]
   \(\int \genfrac {}{}{}{}{-3-2 (1+k^2) x+(1+k^2) x^2+4 k^2 x^3+k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d-(2+d) x-(1+d k^2) x^2+d k^2 x^3)} \, dx\) [2381]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{x^3+x^5} (1+x^4+x^8)}{x^4 (-1+x^4)} \, dx\) [2382]
   \(\int \genfrac {}{}{}{}{1}{(b+a x^2) \sqrt [3]{x+x^3}} \, dx\) [2383]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\) [2384]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\) [2385]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{x+x^3} (b+a x^6)}{d+c x^6} \, dx\) [2386]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{x+x^3} (b+a x^6)}{d+c x^6} \, dx\) [2387]
   \(\int \genfrac {}{}{}{}{(-1+2 x^6) \sqrt [3]{x+x^7}}{(1-2 x^2+x^6) (1-x^2+x^6)} \, dx\) [2388]
   \(\int \genfrac {}{}{}{}{(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^3+a (q+p x^3)^3)}{x^6} \, dx\) [2389]
   \(\int \genfrac {}{}{}{}{-1+(-1+2 k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(2+b) x+(1+b k) x^2)} \, dx\) [2390]
   \(\int \genfrac {}{}{}{}{-3+2 (1+k^2) x+(1+k^2) x^2-4 k^2 x^3+k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(2+d) x+(1+d k^2) x^2+d k^2 x^3)} \, dx\) [2391]
   \(\int \genfrac {}{}{}{}{b-3 a x^3+3 x^6}{x^6 (-b+2 a x^3) \sqrt [4]{-b x+a x^4}} \, dx\) [2392]
   \(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (b x^6+a (q+p x^3)^3)}{x^{11}} \, dx\) [2393]
   \(\int \genfrac {}{}{}{}{x \sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\) [2394]
   \(\int \genfrac {}{}{}{}{x \sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\) [2395]
   \(\int \genfrac {}{}{}{}{x^2}{\sqrt {\genfrac {}{}{}{}{b+a x}{d+c x}}} \, dx\) [2396]
   \(\int \genfrac {}{}{}{}{b+2 a x}{(-b+a x) (2 b+a x) \sqrt [4]{-1+b x+a x^2}} \, dx\) [2397]
   \(\int \genfrac {}{}{}{}{-1+a k x+k x^2}{(1+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\) [2398]
   \(\int \genfrac {}{}{}{}{(-b+x^3) (b+x^3)}{\sqrt [3]{a x^2+x^3}} \, dx\) [2399]
   \(\int \genfrac {}{}{}{}{x}{(1-x^2) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\) [2400]