3.26.1 \(\int \genfrac {}{}{}{}{\sqrt [3]{-x^2+x^4}}{x (1+x^2)} \, dx\) [2501]
  3.26.2 \(\int \genfrac {}{}{}{}{b+a x^6}{x^3 (-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\) [2502]
  3.26.3 \(\int \genfrac {}{}{}{}{\sqrt {a x+\sqrt {-b+a x}}}{x^2 \sqrt {-b+a x}} \, dx\) [2503]
  3.26.4 \(\int \genfrac {}{}{}{}{3+x}{\sqrt [3]{-1+x^2} (5-x+2 x^2)} \, dx\) [2504]
  3.26.5 \(\int \genfrac {}{}{}{}{(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{x^2 \sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x+(-b+k) x^2)} \, dx\) [2505]
  3.26.6 \(\int \genfrac {}{}{}{}{(-2+x^3) \sqrt [3]{x+x^3+x^4}}{(1+x^3) (1-x^2+x^3)} \, dx\) [2506]
  3.26.7 \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx\) [2507]
  3.26.8 \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx\) [2508]
  3.26.9 \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (-1+2 x^6)}{x^6 (-1+2 x^3)} \, dx\) [2509]
  3.26.10 \(\int \genfrac {}{}{}{}{-b+a x^4}{(b+a x^4) \sqrt [4]{b^2+c x^4+a^2 x^8}} \, dx\) [2510]
  3.26.11 \(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {1+x}}}{\sqrt {1+x} (1+x^2)} \, dx\) [2511]
  3.26.12 \(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {1+x}}}{\sqrt {1+x} (1+x^2)} \, dx\) [2512]
  3.26.13 \(\int \genfrac {}{}{}{}{(2+x)^2 \sqrt [3]{-19+66 x-30 x^2+9 x^3}}{(-3+2 x)^2 (-5+6 x-6 x^2+x^3)} \, dx\) [2513]
  3.26.14 \(\int \genfrac {}{}{}{}{1+x^3}{(-1+x^3) \sqrt [3]{x^2+x^4}} \, dx\) [2514]
  3.26.15 \(\int \genfrac {}{}{}{}{x (4 a b-3 (a+b) x+2 x^2)}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a b d+(a+b) d x-d x^2+x^4)} \, dx\) [2515]
  3.26.16 \(\int \genfrac {}{}{}{}{\sqrt {b+a x^4}}{-b+a x^4} \, dx\) [2516]
  3.26.17 \(\int \genfrac {}{}{}{}{1+x^2}{(-1+x+x^2) \sqrt [3]{-1+x^6}} \, dx\) [2517]
  3.26.18 \(\int \genfrac {}{}{}{}{1+x^2}{(-1+x+x^2) \sqrt [3]{-1+x^6}} \, dx\) [2518]
  3.26.19 \(\int \genfrac {}{}{}{}{x^3 \sqrt [3]{-x^2+x^3}}{1+x^6} \, dx\) [2519]
  3.26.20 \(\int \genfrac {}{}{}{}{b-2 c x^4+2 a x^8}{\sqrt [4]{-b+a x^4} (-2 b-c x^4+2 a x^8)} \, dx\) [2520]
  3.26.21 \(\int \genfrac {}{}{}{}{b-2 c x^4+2 a x^8}{\sqrt [4]{-b+a x^4} (-2 b-c x^4+2 a x^8)} \, dx\) [2521]
  3.26.22 \(\int \genfrac {}{}{}{}{1}{x^3 (1+x^3) \sqrt [3]{-x^2+x^3}} \, dx\) [2522]
  3.26.23 \(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt [4]{x^3+x^4}}{1+x^2+x^4} \, dx\) [2523]
  3.26.24 \(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt [4]{x^3+x^4}}{1+x^2+x^4} \, dx\) [2524]
  3.26.25 \(\int \genfrac {}{}{}{}{(-b+a x^2) \sqrt [4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx\) [2525]
  3.26.26 \(\int \genfrac {}{}{}{}{(-b+a x^2) \sqrt [4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx\) [2526]
  3.26.27 \(\int \genfrac {}{}{}{}{(-b^2+a x^2)^2}{(b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\) [2527]
  3.26.28 \(\int \genfrac {}{}{}{}{(-2+(1+k) x) (a-a (1+k) x+(1+a k) x^2)}{(-1+x) \sqrt [3]{(1-x) x (1-k x)} (-1+k x) (b-b (1+k) x+(-1+b k) x^2)} \, dx\) [2528]
  3.26.29 \(\int \genfrac {}{}{}{}{(b+x^3)^3}{\sqrt [3]{a+x^3}} \, dx\) [2529]
  3.26.30 \(\int \genfrac {}{}{}{}{1-x^2+x^3}{(-1-x^2+x^3) \sqrt [3]{x^2+x^3}} \, dx\) [2530]
  3.26.31 \(\int \genfrac {}{}{}{}{1-x^2+x^3}{(-1-x^2+x^3) \sqrt [3]{x^2+x^3}} \, dx\) [2531]
  3.26.32 \(\int \genfrac {}{}{}{}{-3+(1-2 k^2) x+3 k^2 x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(2+d) x-(1+d k^2) x^2+d k^2 x^3)} \, dx\) [2532]
  3.26.33 \(\int \genfrac {}{}{}{}{x^2}{(-b+a x^4) \sqrt {b+a x^4}} \, dx\) [2533]
  3.26.34 \(\int \genfrac {}{}{}{}{(-1+x) (-1+k x) (-2+(1+k) x)}{\sqrt [3]{(1-x) x (1-k x)} (b-2 (b+b k) x+(b+4 b k+b k^2) x^2-2 b k (1+k) x^3+(-1+b k^2) x^4)} \, dx\) [2534]
  3.26.35 \(\int \genfrac {}{}{}{}{(-g+f x^2) \sqrt {c+\sqrt {b+a x}}}{e+d x^2} \, dx\) [2535]
  3.26.36 \(\int \genfrac {}{}{}{}{\sqrt {b^2+a^2 x^2}}{d+c x^2+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [2536]
  3.26.37 \(\int \genfrac {}{}{}{}{\sqrt {b^2+a^2 x^2}}{d+c x^2+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [2537]
  3.26.38 \(\int \genfrac {}{}{}{}{\sqrt {1-\sqrt {1-\sqrt {1-\genfrac {}{}{}{}{1}{x}}}}}{x^2} \, dx\) [2538]
  3.26.39 \(\int \genfrac {}{}{}{}{\sqrt [3]{x^2+x^4}}{x (-1+x^2)} \, dx\) [2539]
  3.26.40 \(\int \genfrac {}{}{}{}{1}{(c+d x) \sqrt {b+a^2 x^2} \sqrt {a x-\sqrt {b+a^2 x^2}}} \, dx\) [2540]
  3.26.41 \(\int \genfrac {}{}{}{}{\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x^2 \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2541]
  3.26.42 \(\int \genfrac {}{}{}{}{-1+(2-k) x}{\sqrt [3]{(1-x) x (1-k x)} (b-(1+2 b k) x+(1+b k^2) x^2)} \, dx\) [2542]
  3.26.43 \(\int \genfrac {}{}{}{}{1}{x^6 (-1+x^3) \sqrt [3]{x^2+x^3}} \, dx\) [2543]
  3.26.44 \(\int \genfrac {}{}{}{}{1}{x^6 (-1+x^3) \sqrt [3]{x^2+x^3}} \, dx\) [2544]
  3.26.45 \(\int \genfrac {}{}{}{}{3+(1-2 k^2) x-3 k^2 x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(2+d) x+(1+d k^2) x^2+d k^2 x^3)} \, dx\) [2545]
  3.26.46 \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (8-4 x^3+x^6)}{x^6 (2+x^3)} \, dx\) [2546]
  3.26.47 \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (8+2 x^3+x^6)}{x^6 (-2+x^3)} \, dx\) [2547]
  3.26.48 \(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (c x^4+b x^2 (q+p x^3)+a (q+p x^3)^2)}{x^9} \, dx\) [2548]
  3.26.49 \(\int \genfrac {}{}{}{}{-b+a x^2}{\sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\) [2549]
  3.26.50 \(\int \genfrac {}{}{}{}{b+a x^2}{\sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\) [2550]
  3.26.51 \(\int \genfrac {}{}{}{}{-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3}{\sqrt [4]{x (-a+x)^2 (-b+x)^3} (b+(-1+a^2 d) x-2 a d x^2+d x^3)} \, dx\) [2551]
  3.26.52 \(\int \genfrac {}{}{}{}{(b+a x^2) \sqrt [4]{b x^3+a x^4}}{x^2 (-b+a x^2)} \, dx\) [2552]
  3.26.53 \(\int \genfrac {}{}{}{}{a b^3-(6 a-b) b^2 x+9 a b x^2-(4 a+3 b) x^3+2 x^4}{\sqrt [4]{x (-a+x)^2 (-b+x)^3} (-a^2+(2 a-b^3 d) x+(-1+3 b^2 d) x^2-3 b d x^3+d x^4)} \, dx\) [2553]
  3.26.54 \(\int \genfrac {}{}{}{}{\sqrt [4]{-b+a x^4} (b+c x^4+a x^8)}{x^6 (b+2 a x^8)} \, dx\) [2554]
  3.26.55 \(\int \genfrac {}{}{}{}{\sqrt [4]{-b+a x^4} (b+c x^4+a x^8)}{x^6 (b+2 a x^8)} \, dx\) [2555]
  3.26.56 \(\int \genfrac {}{}{}{}{1}{(d+c x) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [2556]
  3.26.57 \(\int \genfrac {}{}{}{}{(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b q x+c x^2+b p x^4+a (q+p x^3)^2)}{x^5} \, dx\) [2557]
  3.26.58 \(\int \genfrac {}{}{}{}{-a (a-2 b)-2 b x+x^2}{((-a+x) (-b+x))^{2/3} (a^2+b d-(2 a+d) x+x^2)} \, dx\) [2558]
  3.26.59 \(\int \genfrac {}{}{}{}{a-2 b+x}{\sqrt [3]{(-a+x) (-b+x)} (b+a^2 d+(-1-2 a d) x+d x^2)} \, dx\) [2559]
  3.26.60 \(\int \genfrac {}{}{}{}{a-2 b+x}{\sqrt [3]{(-a+x) (-b+x)} (b+a^2 d-(1+2 a d) x+d x^2)} \, dx\) [2560]
  3.26.61 \(\int \genfrac {}{}{}{}{-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} (b-(1+2 b) x+(b+k) x^2)} \, dx\) [2561]
  3.26.62 \(\int \genfrac {}{}{}{}{-1+x}{(1+x) \sqrt [3]{-x^2+x^3}} \, dx\) [2562]
  3.26.63 \(\int \genfrac {}{}{}{}{(-1+x+x^3+x^6)^{2/3} (3-2 x+3 x^6)}{(-1+x+x^6) (-1+x-x^3+x^6)} \, dx\) [2563]
  3.26.64 \(\int \genfrac {}{}{}{}{-1-2 x^4+2 x^8}{\sqrt [4]{-1+x^4} (-1-x^4+x^8)} \, dx\) [2564]
  3.26.65 \(\int \genfrac {}{}{}{}{-1+2 x^4+2 x^8}{\sqrt [4]{1+x^4} (-1+x^4+x^8)} \, dx\) [2565]
  3.26.66 \(\int \genfrac {}{}{}{}{-a b+(2 a-b) x}{\sqrt [3]{x (-a+x) (-b+x)} (-a^2+(2 a-b d) x+(-1+d) x^2)} \, dx\) [2566]
  3.26.67 \(\int \genfrac {}{}{}{}{(-4 b+a x^4) \sqrt [4]{-b+a x^4}}{x^6 (-8 b+a x^8)} \, dx\) [2567]
  3.26.68 \(\int \genfrac {}{}{}{}{(-4 b+a x^4) \sqrt [4]{-b+a x^4}}{x^6 (-8 b+a x^8)} \, dx\) [2568]
  3.26.69 \(\int \genfrac {}{}{}{}{x}{(1+x) \sqrt [3]{-x^2+x^3}} \, dx\) [2569]
  3.26.70 \(\int \genfrac {}{}{}{}{\sqrt [3]{-x^2+x^3}}{-1+x^2} \, dx\) [2570]
  3.26.71 \(\int x^2 \sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\) [2571]
  3.26.72 \(\int \genfrac {}{}{}{}{(-b x+a^2 x^2)^{3/2}}{(a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\) [2572]
  3.26.73 \(\int \genfrac {}{}{}{}{-3 k+(-2+k^2) x+3 k x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(2+d) k x-(d+k^2) x^2+d k x^3)} \, dx\) [2573]
  3.26.74 \(\int \genfrac {}{}{}{}{a+b x}{x (-d+c x) \sqrt [4]{-x^3+x^4}} \, dx\) [2574]
  3.26.75 \(\int \genfrac {}{}{}{}{(-4+3 x) \sqrt [4]{\genfrac {}{}{}{}{-a+a x+b x^4}{-c+c x+d x^4}}}{(-1+x) x} \, dx\) [2575]
  3.26.76 \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1-2 x^3+2 x^6)}{x^6 (-1-x^3+2 x^6)} \, dx\) [2576]
  3.26.77 \(\int \genfrac {}{}{}{}{2}{(3+x) (2-8 x+8 x^2)^{2/3}} \, dx\) [2577]
  3.26.78 \(\int \genfrac {}{}{}{}{1-(-3+2 k) x-(4+k) x^2+3 k x^3}{\sqrt [3]{(1-x) x (1-k x)} (-1+(5+b) x-(10+b k) x^2+10 x^3-5 x^4+x^5)} \, dx\) [2578]
  3.26.79 \(\int \genfrac {}{}{}{}{1}{x \sqrt [3]{(1+x) (q+2 q x+x^2)}} \, dx\) [2579]
  3.26.80 \(\int \genfrac {}{}{}{}{-1+2 x+(-2 k+k^2) x^2}{((1-x) x (1-k x))^{2/3} (1-(b+2 k) x+(b+k^2) x^2)} \, dx\) [2580]
  3.26.81 \(\int \genfrac {}{}{}{}{3 k+(-2+k^2) x-3 k x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(2+d) k x+(d+k^2) x^2+d k x^3)} \, dx\) [2581]
  3.26.82 \(\int \genfrac {}{}{}{}{3+2 (1+k^2) x-(1+k^2) x^2-4 k^2 x^3-k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(1+2 d) x-(d+k^2) x^2+k^2 x^3)} \, dx\) [2582]
  3.26.83 \(\int \genfrac {}{}{}{}{\sqrt [4]{\genfrac {}{}{}{}{-1+x}{1+2 x}}-3 (\genfrac {}{}{}{}{-1+x}{1+2 x})^{3/4}}{(-1+x) (1+x)^2 (-1+2 x)} \, dx\) [2583]
  3.26.84 \(\int \genfrac {}{}{}{}{(-q+p x^2) \sqrt {q^2+p^2 x^4}}{b x^3+a (q+p x^2)^3} \, dx\) [2584]
  3.26.85 \(\int \genfrac {}{}{}{}{(-q+p x^2) \sqrt {q^2+p^2 x^4}}{b x^3+a (q+p x^2)^3} \, dx\) [2585]
  3.26.86 \(\int \genfrac {}{}{}{}{(-1+x^2)^2}{(1+x^2)^2 \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}} \, dx\) [2586]
  3.26.87 \(\int \genfrac {}{}{}{}{-3+2 (1+k^2) x+(1+k^2) x^2-4 k^2 x^3+k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d+(-1-2 d) x+(d+k^2) x^2+k^2 x^3)} \, dx\) [2587]
  3.26.88 \(\int \genfrac {}{}{}{}{x^3 (-2+(1+k) x)}{((1-x) x (1-k x))^{2/3} (1-(2+2 k) x+(1+4 k+k^2) x^2-(2 k+2 k^2) x^3+(-b+k^2) x^4)} \, dx\) [2588]
  3.26.89 \(\int \genfrac {}{}{}{}{(1+x^2)^2}{(-1+x^2)^2 \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}} \, dx\) [2589]
  3.26.90 \(\int \genfrac {}{}{}{}{(-1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}}{(1+x^2)^2 \sqrt {1+x^4}} \, dx\) [2590]
  3.26.91 \(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2591]
  3.26.92 \(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [2592]
  3.26.93 \(\int \genfrac {}{}{}{}{(-2+x) \sqrt [3]{x-x^2+x^3}}{(-1+x) (-1+x+x^2)} \, dx\) [2593]
  3.26.94 \(\int \genfrac {}{}{}{}{(1+x^2) \sqrt [3]{x^2+x^3}}{-1+x^2} \, dx\) [2594]
  3.26.95 \(\int \genfrac {}{}{}{}{-b+a x}{x \sqrt [3]{-b^3+a^3 x^3}} \, dx\) [2595]
  3.26.96 \(\int \genfrac {}{}{}{}{(-2+x^3) \sqrt [3]{x+2 x^3+x^4}}{(1+x^3) (1+x^2+x^3)} \, dx\) [2596]
  3.26.97 \(\int \genfrac {}{}{}{}{x^4}{\sqrt [4]{-1+x^4} (1-2 x^4+2 x^8)} \, dx\) [2597]
  3.26.98 \(\int \genfrac {}{}{}{}{(-1+x^4)^{3/4}}{1-2 x^4+2 x^8} \, dx\) [2598]
  3.26.99 \(\int \genfrac {}{}{}{}{x^4}{\sqrt [4]{1+x^4} (1+2 x^4+2 x^8)} \, dx\) [2599]
  3.26.100 \(\int \genfrac {}{}{}{}{(1+x^4)^{3/4}}{1+2 x^4+2 x^8} \, dx\) [2600]