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3.18
Integrals 1701 to 1800
3.18.1
\(\int \frac {x^2 \sqrt [4]{x^3+x^4}}{-1+x} \, dx\)
3.18.2
\(\int \frac {(-b+a x^3) (-b+2 a x^3)}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
3.18.3
\(\int \frac {-b+a x^4+x^8}{x^8 (-b+a x^4) \sqrt [4]{b+a x^4}} \, dx\)
3.18.4
\(\int \frac {1+x^4}{x^4 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
3.18.5
\(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^2 \sqrt {b^2+a x^2}} \, dx\)
3.18.6
\(\int \frac {2+x^2}{x (2-2 x+x^2) \sqrt [3]{1-x+x^2}} \, dx\)
3.18.7
\(\int \frac {-1+x}{x^{10} \sqrt [3]{1+x^3}} \, dx\)
3.18.8
\(\int \frac {1}{x \sqrt [3]{b+a x^3}} \, dx\)
3.18.9
\(\int \frac {(-1-2 (-1+k) x+k x^2) (-1+3 k x-3 k^2 x^2+k^3 x^3)}{(-1+x) x \sqrt [4]{(1-x) x (1-k x)} (-1+(d+3 k) x-(d+3 k^2) x^2+k^3 x^3)} \, dx\)
3.18.10
\(\int \frac {(3+x^4) (-1-x^3+x^4)^{2/3}}{x^3 (-1+x^4)} \, dx\)
3.18.11
\(\int \frac {(1+2 x^2) \sqrt [3]{x+2 x^3}}{x^4 (1+2 x^4)} \, dx\)
3.18.12
\(\int \frac {1}{x-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
3.18.13
\(\int \frac {1}{x-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
3.18.14
\(\int \frac {2-x+x^2}{\sqrt [3]{-1+x^2} (3+4 x+x^2)} \, dx\)
3.18.15
\(\int \frac {x (-1+k x) (-1+2 (-1+k) x+k x^2)}{(-1+x) ((1-x) x (1-k x))^{3/4} (-d+(1+3 d) x-(3 d+k) x^2+d x^3)} \, dx\)
3.18.16
\(\int \frac {(-1+x) x (-1-2 (-1+k) x+k x^2)}{((1-x) x (1-k x))^{3/4} (-1+k x) (-d+(1+3 d k) x-(1+3 d k^2) x^2+d k^3 x^3)} \, dx\)
3.18.17
\(\int \frac {(4+x^2) \sqrt [3]{-2 x+x^3}}{x^4 (-4-4 x^2+x^4)} \, dx\)
3.18.18
\(\int \frac {(4+x^2) \sqrt [3]{-2 x+x^3}}{x^4 (-4-4 x^2+x^4)} \, dx\)
3.18.19
\(\int \frac {2 b+a x^3}{(-b+x^2+a x^3) \sqrt [4]{-b x^2+a x^5}} \, dx\)
3.18.20
\(\int \frac {b+a x^2}{(-b+x+a x^2) \sqrt [4]{-b x^3+a x^5}} \, dx\)
3.18.21
\(\int \frac {b+a x^4}{(-b+x^2+a x^4) \sqrt [4]{-b x^2+a x^6}} \, dx\)
3.18.22
\(\int \frac {b+2 a x^3}{(-b+x+a x^3) \sqrt [4]{-b x^3+a x^6}} \, dx\)
3.18.23
\(\int \frac {1}{\sqrt [4]{-b+a x^4} (-b-x^4+a x^8)} \, dx\)
3.18.24
\(\int \frac {1}{\sqrt [4]{-b+a x^4} (-b-x^4+a x^8)} \, dx\)
3.18.25
\(\int \frac {b+a x^4}{\sqrt [4]{-b+a x^4} (b+c x^4+a x^8)} \, dx\)
3.18.26
\(\int \frac {b+a x^4}{\sqrt [4]{-b+a x^4} (b+c x^4+a x^8)} \, dx\)
3.18.27
\(\int \frac {(1+x^5) \sqrt [3]{1+x^3+x^5} (-3+2 x^5)}{x^2 (2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10})} \, dx\)
3.18.28
\(\int \frac {(1+x^5) \sqrt [3]{1+x^3+x^5} (-3+2 x^5)}{x^2 (2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10})} \, dx\)
3.18.29
\(\int x^4 \sqrt [3]{-x+x^3} \, dx\)
3.18.30
\(\int \frac {x}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
3.18.31
\(\int \frac {\sqrt {b x+a x^3}}{-b^2+a^2 x^4} \, dx\)
3.18.32
\(\int \frac {x^{19}}{\sqrt [3]{-1+x^6}} \, dx\)
3.18.33
\(\int x^{15} \sqrt [3]{-1+x^6} \, dx\)
3.18.34
\(\int \frac {x^{19}}{\sqrt [3]{1+x^6}} \, dx\)
3.18.35
\(\int x^{15} \sqrt [3]{1+x^6} \, dx\)
3.18.36
\(\int \frac {-b-a x^3+x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
3.18.37
\(\int \frac {-3-x^4+3 x^6}{(1-x^4+x^6) \sqrt [3]{1-x^3-x^4+x^6}} \, dx\)
3.18.38
\(\int \frac {-b+a x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
3.18.39
\(\int \frac {b+a x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
3.18.40
\(\int \frac {\sqrt [4]{x^2+x^4} (-1-x^4+x^8)}{-1+x^4} \, dx\)
3.18.41
\(\int \frac {-b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b-a x^4+x^8)} \, dx\)
3.18.42
\(\int \frac {-b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b-a x^4+x^8)} \, dx\)
3.18.43
\(\int \frac {\sqrt {c x^2-x \sqrt {-b x+a x^2}}}{x^3 \sqrt {-b x+a x^2}} \, dx\)
3.18.44
\(\int \frac {b+x^3}{\sqrt [3]{a+x^3}} \, dx\)
3.18.45
\(\int \frac {b+a x^2}{\sqrt [3]{x+x^3}} \, dx\)
3.18.46
\(\int \sqrt [3]{-x^2+x^3} \, dx\)
3.18.47
\(\int x^2 \sqrt [3]{x^2+x^3} \, dx\)
3.18.48
\(\int \frac {x^4}{(1+x^4)^2 \sqrt [4]{x^2+x^4}} \, dx\)
3.18.49
\(\int \frac {x^4}{(1+x^4)^2 \sqrt [4]{x^2+x^4}} \, dx\)
3.18.50
\(\int \frac {(-3+x^4) (1-x^3+x^4) (1+x^3+x^4)^{2/3}}{x^6 (1+x^4)} \, dx\)
3.18.51
\(\int \frac {-b+2 a x^4}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
3.18.52
\(\int \frac {-b+2 a x^4}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
3.18.53
\(\int \frac {1+x^2}{(-1+x^2) \sqrt [3]{x+x^5}} \, dx\)
3.18.54
\(\int \frac {(-1+x^2) \sqrt [4]{x^2+x^6}}{x^2 (1+x^2)} \, dx\)
3.18.55
\(\int \frac {(-1+x^2) \sqrt [4]{x^2+x^6}}{x^2 (1+x^2)} \, dx\)
3.18.56
\(\int \frac {(-1+x^3)^{2/3} (1-5 x^3+4 x^6)}{x^6 (-1+2 x^3)^2} \, dx\)
3.18.57
\(\int \frac {\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x-\sqrt {1+x}} \, dx\)
3.18.58
\(\int \frac {\sqrt {b+a x}}{\sqrt {a b x+\sqrt {b+a x}}} \, dx\)
3.18.59
\(\int \frac {\sqrt {b+a^2 x^4}}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
3.18.60
\(\int \frac {1}{(f+e x) \sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\)
3.18.61
\(\int \frac {-a b+(-a+2 b) x}{\sqrt [4]{x (-a+x) (-b+x)^2} (-b^2+(2 b-a d) x+(-1+d) x^2)} \, dx\)
3.18.62
\(\int x^{13} \sqrt [3]{-1+x^3} \, dx\)
3.18.63
\(\int \frac {a b^2-2 (2 a-b) b x+(3 a-2 b) x^2}{\sqrt [4]{x (-a+x) (-b+x)^2} (a^3+(-3 a^2+b^2 d) x+(3 a-2 b d) x^2+(-1+d) x^3)} \, dx\)
3.18.64
\(\int \frac {\sqrt [3]{x+2 x^3} (-1+x^4)}{x^4 (2-x^2+x^4)} \, dx\)
3.18.65
\(\int \frac {b+2 a x^4}{(-b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
3.18.66
\(\int \frac {b+2 a x^4}{(-b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
3.18.67
\(\int \frac {(1+x^6) (-1-x^3+x^6)^{2/3}}{x^3 (-1+x^6)} \, dx\)
3.18.68
\(\int \frac {(4+x^6) \sqrt [4]{-2-x^4+x^6}}{x^2 (-2+x^6)} \, dx\)
3.18.69
\(\int \sqrt [4]{b x^7+a x^8} \, dx\)
3.18.70
\(\int \frac {-1+x^{10}}{\sqrt {1+x^4} (1+x^{10})} \, dx\)
3.18.71
\(\int \frac {1+x^{10}}{\sqrt {1+x^4} (-1+x^{10})} \, dx\)
3.18.72
\(\int \frac {1+x^{16}}{\sqrt {1+x^4} (-1+x^{16})} \, dx\)
3.18.73
\(\int \frac {\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{1-\sqrt {b+a x}} \, dx\)
3.18.74
\(\int x \sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}} \, dx\)
3.18.75
\(\int \frac {(-q+p x^2) \sqrt {q^2+p^2 x^4} (b x^3+a (q+p x^2)^3)}{x^6} \, dx\)
3.18.76
\(\int \frac {(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\)
3.18.77
\(\int \frac {x \sqrt {1+x}}{x+\sqrt {1+\sqrt {1+x}}} \, dx\)
3.18.78
\(\int \frac {\sqrt [3]{-x+x^3} (8-10 x^2+x^4)}{x^4 (4-2 x^2+x^4)} \, dx\)
3.18.79
\(\int \frac {\sqrt [3]{-x+x^3} (8-10 x^2+x^4)}{x^4 (4-2 x^2+x^4)} \, dx\)
3.18.80
\(\int \frac {-1+x^2}{(1+x^2) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
3.18.81
\(\int \frac {-1+x^2}{(1+x^2) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
3.18.82
\(\int \frac {-1+x^4}{(1+x^4) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
3.18.83
\(\int \frac {-1+x^4}{(1+x^4) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
3.18.84
\(\int \frac {b+a x^8}{x^6 (-b+a x^4) (b+a x^4)^{3/4}} \, dx\)
3.18.85
\(\int \frac {-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-2 b-c x^4+2 a x^8)} \, dx\)
3.18.86
\(\int \frac {-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-2 b-c x^4+2 a x^8)} \, dx\)
3.18.87
\(\int \frac {-a b-a c+3 b c+2 (a-b-c) x+x^2}{\sqrt [4]{(-a+x) (-b+x) (-c+x)} (-a^3-b c d+(3 a^2+b d+c d) x-(3 a+d) x^2+x^3)} \, dx\)
3.18.88
\(\int \frac {1}{(-b+a x) \sqrt [4]{b^2 x+a^2 x^3}} \, dx\)
3.18.89
\(\int \frac {(2+x^2) (-2-2 x+x^2) \sqrt {4-3 x^2+x^4}}{x^2 (-2+x^2) (-4+x+2 x^2)} \, dx\)
3.18.90
\(\int \frac {1+x}{(-1+x) \sqrt [3]{x^2+x^4}} \, dx\)
3.18.91
\(\int \frac {-b^2+a^4 x^4}{\sqrt {b x+a^2 x^3} (b^2+a^4 x^4)} \, dx\)
3.18.92
\(\int \frac {-1+x^2}{(1+x^2) \sqrt [3]{x+x^5}} \, dx\)
3.18.93
\(\int \frac {(1+x^4) \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\)
3.18.94
\(\int \frac {(1+x^4) \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\)
3.18.95
\(\int \frac {1-2 x^4+2 x^8}{\sqrt [4]{-1+x^4} (-2-x^4+2 x^8)} \, dx\)
3.18.96
\(\int \frac {\sqrt {-x+x^2} \sqrt {x^2-x \sqrt {-x+x^2}}}{x^3} \, dx\)
3.18.97
\(\int \frac {b+2 a x}{\sqrt [4]{c+b x+a x^2} (5 c+4 b x+4 a x^2)} \, dx\)
3.18.98
\(\int x^6 \sqrt [3]{-x+x^3} \, dx\)
3.18.99
\(\int \frac {1}{\sqrt [3]{-1-x+x^2+x^3}} \, dx\)
3.18.100
\(\int \frac {1+2 x^4}{(-1+x^4) \sqrt [4]{-x^2+x^4}} \, dx\)
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