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3.28
Integrals 2701 to 2800
\(\int \genfrac {}{}{}{}{\sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}}{1+x^2} \, dx\) [2701]
\(\int \genfrac {}{}{}{}{x}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\) [2702]
\(\int \genfrac {}{}{}{}{x}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\) [2703]
\(\int \genfrac {}{}{}{}{\sqrt {b+a x} \sqrt {1+\sqrt {b+a x}}}{x^2 \sqrt {1+\sqrt {1+\sqrt {b+a x}}}} \, dx\) [2704]
\(\int \genfrac {}{}{}{}{\sqrt {b+a x} \sqrt {1+\sqrt {b+a x}}}{x^2 \sqrt {1+\sqrt {1+\sqrt {b+a x}}}} \, dx\) [2705]
\(\int \genfrac {}{}{}{}{x^4 \sqrt [4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx\) [2706]
\(\int \genfrac {}{}{}{}{x^4 \sqrt [4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx\) [2707]
\(\int \genfrac {}{}{}{}{(b+a x) (-3 a q+4 b p x^3+a p x^4)}{(q+p x^4)^{2/3} (b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+a^3 c x^3+d p x^4)} \, dx\) [2708]
\(\int \genfrac {}{}{}{}{\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x^7 (b^2+a^2 x^6)} \, dx\) [2709]
\(\int \genfrac {}{}{}{}{(-2+x^4) \sqrt {2+x^4}}{(2+x^2+x^4) (2+2 x^2+x^4)} \, dx\) [2710]
\(\int \genfrac {}{}{}{}{x^2 (-2+x^8) \sqrt [4]{2-2 x^4+x^8}}{(2+x^8) (4-x^4+2 x^8)} \, dx\) [2711]
\(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\) [2712]
\(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\) [2713]
\(\int \genfrac {}{}{}{}{1}{\sqrt {-b+a^2 x^2} \sqrt [3]{a x^2+x \sqrt {-b+a^2 x^2}}} \, dx\) [2714]
\(\int \genfrac {}{}{}{}{\sqrt {-b+a x}}{1+\sqrt {a x+\sqrt {-b+a x}}} \, dx\) [2715]
\(\int x \sqrt {1+\sqrt {2}+\sqrt {2} x+x^2} \, dx\) [2716]
\(\int \genfrac {}{}{}{}{-a x+x^2}{(x^2 (-a+x))^{2/3} (a^2-2 a x+(1-d) x^2)} \, dx\) [2717]
\(\int \genfrac {}{}{}{}{x}{\sqrt [3]{x^2 (-a+x)} (-a^2+2 a x+(-1+d) x^2)} \, dx\) [2718]
\(\int \genfrac {}{}{}{}{-a b x^2+x^4}{(x^2 (-a+x) (-b+x))^{2/3} (a^2 b^2-2 a b (a+b) x+(a^2+4 a b+b^2-d) x^2-2 (a+b) x^3+x^4)} \, dx\) [2719]
\(\int \genfrac {}{}{}{}{\sqrt [4]{\genfrac {}{}{}{}{1+4 x^2+a x^2+6 x^4+4 a x^4+4 x^6+6 a x^6+x^8+4 a x^8+a x^{10}}{x^2}}}{x} \, dx\) [2720]
\(\int \genfrac {}{}{}{}{\sqrt [3]{2-8 x+8 x^2}}{3+x} \, dx\) [2721]
\(\int \genfrac {}{}{}{}{(b+a x) (-a q+b p x^2)}{(q+p x^3)^{2/3} (b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+(a^3 c+d p) x^3)} \, dx\) [2722]
\(\int \genfrac {}{}{}{}{(-b+x) (-a (a-2 b)-2 b x+x^2)}{((-a+x) (-b+x))^{2/3} (a^4-b^2 d-2 (2 a^3-b d) x+(6 a^2-d) x^2-4 a x^3+x^4)} \, dx\) [2723]
\(\int \genfrac {}{}{}{}{\sqrt {1+x^5} (2+x^5)}{x^6 (-1-x^5+a x^{10})} \, dx\) [2724]
\(\int \genfrac {}{}{}{}{(-2+x^5) \sqrt {-1+x^5}}{x^6 (1-x^5+a x^{10})} \, dx\) [2725]
\(\int \genfrac {}{}{}{}{1}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\) [2726]
\(\int \genfrac {}{}{}{}{1}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\) [2727]
\(\int \genfrac {}{}{}{}{x (x^2 c_3-c_4)}{\sqrt {\genfrac {}{}{}{}{x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}} (x+3 x^2 c_3+3 c_4) (-x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2)} \, dx\) [2728]
\(\int \genfrac {}{}{}{}{1}{(-b+a x^4)^2 \sqrt [4]{-b x^2+a x^4}} \, dx\) [2729]
\(\int \genfrac {}{}{}{}{1}{(-b+a x^4)^2 \sqrt [4]{-b x^2+a x^4}} \, dx\) [2730]
\(\int \genfrac {}{}{}{}{(-2 q+p x^3) (a q+b x^2+a p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^5 (c q+d x^2+c p x^3)} \, dx\) [2731]
\(\int -\genfrac {}{}{}{}{(-1+x) x (-1+2 x+(-2 k+k^2) x^2)}{((1-x) x (1-k x))^{2/3} (1-4 k x+(-b+6 k^2) x^2+(2 b-4 k^3) x^3+(-b+k^4) x^4)} \, dx\) [2732]
\(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (b x^8+a (q+p x^3)^4)}{x^{13}} \, dx\) [2733]
\(\int \genfrac {}{}{}{}{x^2}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\) [2734]
\(\int \genfrac {}{}{}{}{x^2}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\) [2735]
\(\int \genfrac {}{}{}{}{1}{x \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx\) [2736]
\(\int \genfrac {}{}{}{}{1-x+x^2}{(-1+x^2) \sqrt [3]{x^2+x^4}} \, dx\) [2737]
\(\int \genfrac {}{}{}{}{1+x+x^2}{(-1+x^2) \sqrt [3]{x^2+x^4}} \, dx\) [2738]
\(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {1-x-x^2+x^3+x^4}}{x^2 (1+x^2)} \, dx\) [2739]
\(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {1-x-x^2+x^3+x^4}}{x^2 (1+x^2)} \, dx\) [2740]
\(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (4+x^3)}{x^6 (-2-x^3+x^6)} \, dx\) [2741]
\(\int \genfrac {}{}{}{}{\sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\) [2742]
\(\int \genfrac {}{}{}{}{(x+x^2) \sqrt [4]{x^3+x^4}}{-1+x+x^2} \, dx\) [2743]
\(\int \genfrac {}{}{}{}{(b+x^4)^2}{\sqrt [4]{a b^4+4 a b^3 x^4+b^4 x^4+6 a b^2 x^8+4 b^3 x^8+4 a b x^{12}+6 b^2 x^{12}+a x^{16}+4 b x^{16}+x^{20}}} \, dx\) [2744]
\(\int \genfrac {}{}{}{}{(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^4+a (q+p x^3)^4)}{x^7} \, dx\) [2745]
\(\int \genfrac {}{}{}{}{1-\sqrt {x-\sqrt {1+x^2}}}{x^4-2 x^2 \sqrt {1+x^2}} \, dx\) [2746]
\(\int \genfrac {}{}{}{}{1}{\sqrt {-b+a^2 x^2} \sqrt [6]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [2747]
\(\int \genfrac {}{}{}{}{(1-2 k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d+(1-2 d k^2) x^2+d k^4 x^4)} \, dx\) [2748]
\(\int \genfrac {}{}{}{}{(2-k^2) x-2 x^3+k^2 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d+(-2+d k^2) x^2+x^4)} \, dx\) [2749]
\(\int \genfrac {}{}{}{}{(-1+x^4) \sqrt [4]{-x^2+x^4}}{-1-x^2+x^4} \, dx\) [2750]
\(\int \genfrac {}{}{}{}{1+(3-2 k) x-(4+k) x^2+3 k x^3}{\sqrt [3]{(1-x) x (1-k x)} (-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5)} \, dx\) [2751]
\(\int \genfrac {}{}{}{}{x^3}{\sqrt [3]{-x^2+x^3} (-1+x^6)} \, dx\) [2752]
\(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\) [2753]
\(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\) [2754]
\(\int \genfrac {}{}{}{}{1}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [2755]
\(\int \genfrac {}{}{}{}{(-b+x) (a b-2 b x+x^2)}{(x (-a+x) (-b+x)^2)^{2/3} (b-(1+a d) x+d x^2)} \, dx\) [2756]
\(\int \genfrac {}{}{}{}{(a-5 b+4 x) (-a^3+3 a^2 x-3 a x^2+x^3)}{((-a+x) (-b+x))^{2/3} (-a^5+b d-(-5 a^4+d) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5)} \, dx\) [2757]
\(\int \genfrac {}{}{}{}{1-x^3 \sqrt [3]{5+4 x}-x^3 (5+4 x)^{2/3}}{1-x \sqrt {5+4 x}} \, dx\) [2758]
\(\int \genfrac {}{}{}{}{x^3 (x^3 c_3-2 c_4) \sqrt {\genfrac {}{}{}{}{x^2 c_0+x^3 c_3+c_4}{x^2 c_1+x^3 c_3+c_4}}}{(x^2+2 x^3 c_3+2 c_4) (-x^4+x^6 c_3{}^2+2 x^3 c_3 c_4+c_4{}^2)} \, dx\) [2759]
\(\int \genfrac {}{}{}{}{x^5 (2 x^5 c_3-3 c_4) \sqrt {\genfrac {}{}{}{}{x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{(x^3+2 x^5 c_3+2 c_4) (-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2)} \, dx\) [2760]
\(\int \genfrac {}{}{}{}{(-1+x^2)^2 (x+x^3)}{\sqrt {1+x^4} (1-2 x^2+4 x^4-2 x^6+x^8)} \, dx\) [2761]
\(\int \genfrac {}{}{}{}{(-1+x+2 x^2) \sqrt [4]{-x^3+x^4}}{-1-x+x^2} \, dx\) [2762]
\(\int \genfrac {}{}{}{}{(2+x^6) (-1+x^4+x^6)}{\sqrt [4]{-1+x^6} (1-2 x^6+x^8+x^{12})} \, dx\) [2763]
\(\int \genfrac {}{}{}{}{1}{(d+c x)^2 \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [2764]
\(\int \genfrac {}{}{}{}{(1+x^2)^2}{(-1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\) [2765]
\(\int \genfrac {}{}{}{}{a (a b+a c-2 b c)-2 (a^2-b c) x+(2 a-b-c) x^2}{((-a+x) (-b+x) (-c+x))^{2/3} (a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2)} \, dx\) [2766]
\(\int \genfrac {}{}{}{}{1+x^4}{(-1+x^4) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\) [2767]
\(\int \genfrac {}{}{}{}{(-1+x^2)^2}{(1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\) [2768]
\(\int \genfrac {}{}{}{}{2 a b^2-b (2 a+b) x+x^3}{\sqrt [3]{x (-a+x) (-b+x)^2} (-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3)} \, dx\) [2769]
\(\int \genfrac {}{}{}{}{-d+c x}{x \sqrt [3]{-b+a x^3}} \, dx\) [2770]
\(\int \genfrac {}{}{}{}{-b^4+c^2 x^2+a^4 x^4}{\sqrt {-b^4+a^4 x^4} (b^4+a^4 x^4)} \, dx\) [2771]
\(\int \genfrac {}{}{}{}{x^2}{(1-x^4) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\) [2772]
\(\int \genfrac {}{}{}{}{x (-b+x) (-a^2 b+2 a^2 x+(-2 a+b) x^2)}{(x (-a+x) (-b+x))^{2/3} (-a^4+4 a^3 x+(-6 a^2+b^2 d) x^2+2 (2 a-b d) x^3+(-1+d) x^4)} \, dx\) [2773]
\(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (8-8 x^3+x^6)}{x^6 (-4+x^3) (-2+x^3)} \, dx\) [2774]
\(\int \genfrac {}{}{}{}{(c+(a x+\sqrt {-b+a^2 x^2})^{3/4})^{4/3}}{\sqrt {-b+a^2 x^2}} \, dx\) [2775]
\(\int \genfrac {}{}{}{}{1}{(-b+a x) \sqrt [3]{b^3+a^3 x^3}} \, dx\) [2776]
\(\int \genfrac {}{}{}{}{\sqrt [3]{a x^2+b x \sqrt {-\genfrac {}{}{}{}{a}{b^2}+\genfrac {}{}{}{}{a^2 x^2}{b^2}}}}{\sqrt {-\genfrac {}{}{}{}{a}{b^2}+\genfrac {}{}{}{}{a^2 x^2}{b^2}}} \, dx\) [2777]
\(\int \genfrac {}{}{}{}{\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\) [2778]
\(\int \genfrac {}{}{}{}{\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\) [2779]
\(\int \genfrac {}{}{}{}{-b+x}{((-a+x) (-b+x)^2)^{2/3} (b-a d+(-1+d) x)} \, dx\) [2780]
\(\int \genfrac {}{}{}{}{-a q x+b p x^3}{\sqrt {q+p x^4} (b^2 c+d q+2 a b c x^2+(a^2 c+d p) x^4)} \, dx\) [2781]
\(\int \genfrac {}{}{}{}{(b+a x)^2 (-2 a q+3 b p x^2+a p x^3)}{\sqrt {q+p x^3} (b^4 c+d q^2+4 a b^3 c x+6 a^2 b^2 c x^2+(4 a^3 b c+2 d p q) x^3+a^4 c x^4+d p^2 x^6)} \, dx\) [2782]
\(\int \genfrac {}{}{}{}{(1+x^2) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [2783]
\(\int \genfrac {}{}{}{}{(1+x^2) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [2784]
\(\int \genfrac {}{}{}{}{-1+k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (a+b x^2+a k^4 x^4)} \, dx\) [2785]
\(\int \genfrac {}{}{}{}{x^5 (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} (-a^2+2 a x-x^2+d x^8)} \, dx\) [2786]
\(\int \genfrac {}{}{}{}{\sqrt {1-x}}{8 (1+x)^{7/2}} \, dx\) [2787]
\(\int \genfrac {}{}{}{}{2 a b^2-b (2 a+b) x+x^3}{\sqrt [3]{x (-a+x) (-b+x)^2} (-a b^2 d+b (2 a+b) d x-(1+a d+2 b d) x^2+d x^3)} \, dx\) [2788]
\(\int \genfrac {}{}{}{}{(-x+x^2) \sqrt [4]{-x^3+x^4}}{-1-x+x^2} \, dx\) [2789]
\(\int \genfrac {}{}{}{}{\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{x \sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\) [2790]
\(\int \genfrac {}{}{}{}{\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{x \sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\) [2791]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [2792]
\(\int \genfrac {}{}{}{}{(-1+x) (-1+k x) (-2 x+(1+k) x^2)}{((1-x) x (1-k x))^{2/3} (b-2 b (1+k) x+(b+4 b k+b k^2) x^2-2 b k (1+k) x^3+(-1+b k^2) x^4)} \, dx\) [2793]
\(\int \genfrac {}{}{}{}{(-1+2 (-2+k) x+3 k x^2) (-1+3 x-3 x^2+x^3)}{((1-x) x (1-k x))^{2/3} (-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5)} \, dx\) [2794]
\(\int \genfrac {}{}{}{}{\sqrt [4]{2 b+a x^4} (-4 b+a x^8)}{x^6 (-4 b+c x^4+a x^8)} \, dx\) [2795]
\(\int \genfrac {}{}{}{}{\sqrt [4]{2 b+a x^4} (-4 b+a x^8)}{x^6 (-4 b+c x^4+a x^8)} \, dx\) [2796]
\(\int \genfrac {}{}{}{}{-b^{12}+a^{12} x^{12}}{\sqrt {-b^4+a^4 x^4} (b^{12}+a^{12} x^{12})} \, dx\) [2797]
\(\int \genfrac {}{}{}{}{1}{1-(1+x) \sqrt {c+b x+a x^2}} \, dx\) [2798]
\(\int \genfrac {}{}{}{}{(1-x^4) \sqrt [4]{1-x-4 x^2+4 x^3+6 x^4-6 x^5-4 x^6+4 x^7+x^8-x^9}}{1+x^4} \, dx\) [2799]
\(\int \genfrac {}{}{}{}{-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt [3]{(-a+x) (-b+x)} (b-a^5 d-(1-5 a^4 d) x-10 a^3 d x^2+10 a^2 d x^3-5 a d x^4+d x^5)} \, dx\) [2800]
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