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3.5
Integrals 401 to 500
3.5.1
\(\int \sqrt [4]{-1+3 x-3 x^2+x^3} (-1-2 x+x^2+3 x^3) \, dx\) [401]
3.5.2
\(\int \genfrac {}{}{}{}{(-2 b+a x^3) \sqrt {b+a x^3}}{x^2 (b-x^2+a x^3)} \, dx\) [402]
3.5.3
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{1+x^4}} \, dx\) [403]
3.5.4
\(\int \genfrac {}{}{}{}{-1-2 x+2 x^2}{(1+2 x+4 x^2) \sqrt {x+x^4}} \, dx\) [404]
3.5.5
\(\int \sqrt {x+x^4} \, dx\) [405]
3.5.6
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{-x^2+x^4}} \, dx\) [406]
3.5.7
\(\int \genfrac {}{}{}{}{2 b+a x^2}{\sqrt [4]{b+a x^2} (-b-a x^2+x^4)} \, dx\) [407]
3.5.8
\(\int \genfrac {}{}{}{}{-1+2 x}{\sqrt {-2-2 x+3 x^2-2 x^3+x^4}} \, dx\) [408]
3.5.9
\(\int \genfrac {}{}{}{}{-1+2 x}{\sqrt {-4-4 x+5 x^2-2 x^3+x^4}} \, dx\) [409]
3.5.10
\(\int \genfrac {}{}{}{}{1}{x^4 \sqrt [4]{x^3+x^4}} \, dx\) [410]
3.5.11
\(\int \genfrac {}{}{}{}{x}{\sqrt {-b+a x^4}} \, dx\) [411]
3.5.12
\(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1-x^3+2 x^6)}{x^{12}} \, dx\) [412]
3.5.13
\(\int \genfrac {}{}{}{}{(3+x^4) \sqrt {x-x^5}}{1-2 x^4-x^6+x^8} \, dx\) [413]
3.5.14
\(\int \genfrac {}{}{}{}{-1+x^{16}}{x^8 \sqrt {-1+x^4}} \, dx\) [414]
3.5.15
\(\int \genfrac {}{}{}{}{(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx\) [415]
3.5.16
\(\int \genfrac {}{}{}{}{1+x}{(-1+x) \sqrt {x+x^2+x^3}} \, dx\) [416]
3.5.17
\(\int \genfrac {}{}{}{}{-1+x^2}{(1-x+x^2) \sqrt {x+x^2+x^3}} \, dx\) [417]
3.5.18
\(\int \genfrac {}{}{}{}{-1+x}{(1+x) \sqrt {1+x^4}} \, dx\) [418]
3.5.19
\(\int \genfrac {}{}{}{}{1+x}{(-1+x) \sqrt {1+x^4}} \, dx\) [419]
3.5.20
\(\int \genfrac {}{}{}{}{1+x}{(-1+x) \sqrt {1+x^2+x^4}} \, dx\) [420]
3.5.21
\(\int \genfrac {}{}{}{}{1+x^2}{(-1+x^2) \sqrt {1-x-x^2+x^3+x^4}} \, dx\) [421]
3.5.22
\(\int \genfrac {}{}{}{}{x}{\sqrt {11-11 x-3 x^2+2 x^3+x^4}} \, dx\) [422]
3.5.23
\(\int \genfrac {}{}{}{}{1+x}{\sqrt {2-5 x-3 x^2+2 x^3+x^4}} \, dx\) [423]
3.5.24
\(\int \genfrac {}{}{}{}{x}{\sqrt {-3+3 x-3 x^2+2 x^3+x^4}} \, dx\) [424]
3.5.25
\(\int \genfrac {}{}{}{}{\sqrt {1-x^6} (2+x^6)}{x^3 (-1+x^4+x^6)} \, dx\) [425]
3.5.26
\(\int \genfrac {}{}{}{}{\sqrt {x}}{(-2+x^2)^{3/4}} \, dx\) [426]
3.5.27
\(\int \genfrac {}{}{}{}{a+x}{(-1+2 b+2 a x+x^2) \sqrt [4]{2 b+2 a x+x^2}} \, dx\) [427]
3.5.28
\(\int \genfrac {}{}{}{}{1}{\sqrt {c+b x+a x^2}} \, dx\) [428]
3.5.29
\(\int x^{11} \sqrt [3]{-1+x^3} \, dx\) [429]
3.5.30
\(\int \genfrac {}{}{}{}{-1-2 x+x^2}{(1+2 x+3 x^2) \sqrt {-x+x^3}} \, dx\) [430]
3.5.31
\(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {-1-4 x-5 x^2-4 x^3-x^4}}{(1+x+x^2) (1+3 x+x^2)^2} \, dx\) [431]
3.5.32
\(\int \genfrac {}{}{}{}{-1+x^4}{x^3 \sqrt {1+x^4}} \, dx\) [432]
3.5.33
\(\int \genfrac {}{}{}{}{-1+x^3}{x^6 (1+x^3) \sqrt [4]{x+x^4}} \, dx\) [433]
3.5.34
\(\int \genfrac {}{}{}{}{\sqrt {x+x^4}}{x^3} \, dx\) [434]
3.5.35
\(\int \genfrac {}{}{}{}{1}{x^8 \sqrt [4]{x^2+x^4}} \, dx\) [435]
3.5.36
\(\int \genfrac {}{}{}{}{1-2 x}{\sqrt {5+5 x-4 x^2-2 x^3+x^4}} \, dx\) [436]
3.5.37
\(\int \genfrac {}{}{}{}{1}{x^4 \sqrt [4]{-x^3+x^4}} \, dx\) [437]
3.5.38
\(\int \genfrac {}{}{}{}{1+2 x}{\sqrt {-4-3 x-2 x^2+2 x^3+x^4}} \, dx\) [438]
3.5.39
\(\int \genfrac {}{}{}{}{4 b+a x^3}{\sqrt [4]{b+a x^3} (-b-a x^3+x^4)} \, dx\) [439]
3.5.40
\(\int \genfrac {}{}{}{}{x^8}{\sqrt {-1+x^6}} \, dx\) [440]
3.5.41
\(\int \genfrac {}{}{}{}{\sqrt {-1+x^6}}{x^4} \, dx\) [441]
3.5.42
\(\int x^2 \sqrt {-1+x^6} \, dx\) [442]
3.5.43
\(\int \genfrac {}{}{}{}{x^8}{\sqrt {1+x^6}} \, dx\) [443]
3.5.44
\(\int \genfrac {}{}{}{}{\sqrt {1+x^6}}{x^4} \, dx\) [444]
3.5.45
\(\int \genfrac {}{}{}{}{1+x^6}{x^6 (1+x^3) \sqrt [4]{x+x^4}} \, dx\) [445]
3.5.46
\(\int x \sqrt {x+x^6} \, dx\) [446]
3.5.47
\(\int \genfrac {}{}{}{}{-2 b c+a c x^6}{\sqrt [4]{b+a x^6} (b-c^4 x^4+a x^6)} \, dx\) [447]
3.5.48
\(\int \genfrac {}{}{}{}{1}{\sqrt {x+\sqrt {1+x^2}}} \, dx\) [448]
3.5.49
\(\int \genfrac {}{}{}{}{\sqrt [4]{1+x^2}}{x} \, dx\) [449]
3.5.50
\(\int \genfrac {}{}{}{}{\sqrt {-1+x^3}}{x^7} \, dx\) [450]
3.5.51
\(\int \genfrac {}{}{}{}{-b+a x^2}{(b+c x+a x^2) \sqrt {b x+a x^3}} \, dx\) [451]
3.5.52
\(\int \genfrac {}{}{}{}{-1+x}{\sqrt {-2-x+6 x^2-4 x^3+x^4}} \, dx\) [452]
3.5.53
\(\int \genfrac {}{}{}{}{\sqrt {-1+x^6}}{x^{13}} \, dx\) [453]
3.5.54
\(\int \genfrac {}{}{}{}{-1-2 x^2+2 x^4}{(2-3 x^2+x^4) \sqrt {1+x^6}} \, dx\) [454]
3.5.55
\(\int \genfrac {}{}{}{}{-1+k x}{(1+k x) \sqrt {(1-x) x (1-k^2 x)}} \, dx\) [455]
3.5.56
\(\int \genfrac {}{}{}{}{1+k x}{(-1+k x) \sqrt {(1-x) x (1-k^2 x)}} \, dx\) [456]
3.5.57
\(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {1+x^4}}{x^2 (1+x^2)} \, dx\) [457]
3.5.58
\(\int \genfrac {}{}{}{}{1+x^3}{x^6 (-1+x^3) \sqrt [4]{-x+x^4}} \, dx\) [458]
3.5.59
\(\int \sqrt {-x+x^4} \, dx\) [459]
3.5.60
\(\int \genfrac {}{}{}{}{1}{x^8 \sqrt [4]{-x^2+x^4}} \, dx\) [460]
3.5.61
\(\int \genfrac {}{}{}{}{-1+x}{\sqrt {-1+4 x+2 x^2-4 x^3+x^4}} \, dx\) [461]
3.5.62
\(\int \genfrac {}{}{}{}{\sqrt [4]{-x^3+x^4}}{(-1+x) x} \, dx\) [462]
3.5.63
\(\int \genfrac {}{}{}{}{-2+x^3}{x \sqrt {-1+x^6}} \, dx\) [463]
3.5.64
\(\int \genfrac {}{}{}{}{1+x^3}{x \sqrt {-1+x^6}} \, dx\) [464]
3.5.65
\(\int \genfrac {}{}{}{}{-1+2 x^3}{x \sqrt {-1+x^6}} \, dx\) [465]
3.5.66
\(\int \genfrac {}{}{}{}{1+2 x^3}{x \sqrt {-1+x^6}} \, dx\) [466]
3.5.67
\(\int \genfrac {}{}{}{}{1+4 x^3}{x \sqrt {-1+x^6}} \, dx\) [467]
3.5.68
\(\int \genfrac {}{}{}{}{1+x^6}{x^6 (-1+x^3) \sqrt [4]{-x+x^4}} \, dx\) [468]
3.5.69
\(\int \genfrac {}{}{}{}{x (8 b+5 a x^3)}{\sqrt [4]{b+a x^3} (-b-a x^3+x^8)} \, dx\) [469]
3.5.70
\(\int \sqrt {x+\sqrt {1+x^2}} \, dx\) [470]
3.5.71
\(\int \genfrac {}{}{}{}{a b-x^2}{\sqrt {x (-a+x) (-b+x)} (a b-(a+b+d) x+x^2)} \, dx\) [471]
3.5.72
\(\int \genfrac {}{}{}{}{a b-x^2}{\sqrt {x (-a+x) (-b+x)} (a b d-(1+a d+b d) x+d x^2)} \, dx\) [472]
3.5.73
\(\int \genfrac {}{}{}{}{-1+k x^2}{(1+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\) [473]
3.5.74
\(\int \genfrac {}{}{}{}{1+k x^2}{(-1+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\) [474]
3.5.75
\(\int \genfrac {}{}{}{}{1-2 k^2 x+k^2 x^2}{x \sqrt {(1-x) x (1-k^2 x)} (-1+k^2 x)} \, dx\) [475]
3.5.76
\(\int \genfrac {}{}{}{}{1}{x^7 \sqrt {-1+x^3}} \, dx\) [476]
3.5.77
\(\int \genfrac {}{}{}{}{1}{x^7 \sqrt {1+x^3}} \, dx\) [477]
3.5.78
\(\int \genfrac {}{}{}{}{\sqrt {1+x^3}}{x^7} \, dx\) [478]
3.5.79
\(\int \genfrac {}{}{}{}{1+x^3}{x^7 \sqrt {-1+x^3}} \, dx\) [479]
3.5.80
\(\int \genfrac {}{}{}{}{\sqrt {-1+x^3} (2+x^3)}{x^2 (-2-4 x^2+2 x^3)} \, dx\) [480]
3.5.81
\(\int x^5 \sqrt {b+a x^3} \, dx\) [481]
3.5.82
\(\int \genfrac {}{}{}{}{(-3+x^4) \sqrt [3]{1+x^4} (1+x^3+x^4)}{x^8} \, dx\) [482]
3.5.83
\(\int \genfrac {}{}{}{}{(-3+x^4) (1+x^4)^{2/3} (1+x^3+x^4)}{x^9} \, dx\) [483]
3.5.84
\(\int \genfrac {}{}{}{}{(-1+x^4)^{2/3} (3+x^4) (-2-x^3+2 x^4)}{x^9} \, dx\) [484]
3.5.85
\(\int \genfrac {}{}{}{}{(-1+x^5)^{3/4} (4+x^5) (-1-x^4+x^5)}{x^{12}} \, dx\) [485]
3.5.86
\(\int \genfrac {}{}{}{}{(1+x^5)^{2/3} (1+x^3+x^5) (-3+2 x^5)}{x^9} \, dx\) [486]
3.5.87
\(\int \genfrac {}{}{}{}{(-1+x^5)^{2/3} (-1+x^3+x^5) (3+2 x^5)}{x^9} \, dx\) [487]
3.5.88
\(\int \genfrac {}{}{}{}{(-4+x^5) (1+x^5)^{3/4} (2-x^4+2 x^5)}{x^{12}} \, dx\) [488]
3.5.89
\(\int \genfrac {}{}{}{}{(1+x^5)^{2/3} (-3+2 x^5) (4+3 x^3+4 x^5)}{x^9} \, dx\) [489]
3.5.90
\(\int \genfrac {}{}{}{}{1}{x^{13} \sqrt {-1+x^6}} \, dx\) [490]
3.5.91
\(\int \genfrac {}{}{}{}{-1+x^6}{x^{13} \sqrt {1+x^6}} \, dx\) [491]
3.5.92
\(\int \genfrac {}{}{}{}{\sqrt {1+x^6}}{x^{13}} \, dx\) [492]
3.5.93
\(\int \genfrac {}{}{}{}{1+x^6}{x^{13} \sqrt {-1+x^6}} \, dx\) [493]
3.5.94
\(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^6} (1+x^6) (-1+x^3+x^6)}{x^8} \, dx\) [494]
3.5.95
\(\int \genfrac {}{}{}{}{(-1+x^6)^{3/4} (2+x^6) (-1-x^4+x^6)}{x^{12}} \, dx\) [495]
3.5.96
\(\int \genfrac {}{}{}{}{(-2+x^6) (1+x^6)^{3/4} (1-x^4+x^6)}{x^{12}} \, dx\) [496]
3.5.97
\(\int \genfrac {}{}{}{}{-2 x+3 x^2}{\sqrt {5-4 x^2+4 x^3+x^4-2 x^5+x^6}} \, dx\) [497]
3.5.98
\(\int \genfrac {}{}{}{}{-2+5 x^6}{x \sqrt {-1+x^6} (2+x^6)} \, dx\) [498]
3.5.99
\(\int \genfrac {}{}{}{}{-1+10 x^6}{x \sqrt {-1+x^6} (-1+4 x^6)} \, dx\) [499]
3.5.100
\(\int \genfrac {}{}{}{}{2+x+x^2}{x^2 (1+x^2)^{3/4}} \, dx\) [500]
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