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3.16
Integrals 1501 to 1600
3.16.1
\(\int \genfrac {}{}{}{}{(2+x)^2}{x (4-2 x+x^2) \sqrt [3]{1+x+x^2}} \, dx\) [1501]
3.16.2
\(\int \genfrac {}{}{}{}{1}{(-2 b+a x^2) \sqrt [4]{-b+a x^2}} \, dx\) [1502]
3.16.3
\(\int \genfrac {}{}{}{}{-1+x}{x^7 \sqrt [3]{1+x^3}} \, dx\) [1503]
3.16.4
\(\int \genfrac {}{}{}{}{3 c+2 b x+a x^2}{\sqrt [3]{c+b x+a x^2} (c+b x+a x^2+x^3)} \, dx\) [1504]
3.16.5
\(\int \genfrac {}{}{}{}{-b+a x^2}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1505]
3.16.6
\(\int \genfrac {}{}{}{}{-b+a x^2}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1506]
3.16.7
\(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1507]
3.16.8
\(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1508]
3.16.9
\(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1509]
3.16.10
\(\int \genfrac {}{}{}{}{x (3+5 x^2)}{\sqrt [3]{1+x^2} (-1+x^3+x^5)} \, dx\) [1510]
3.16.11
\(\int \genfrac {}{}{}{}{(-1+x^5)^{2/3} (3+2 x^5) (-2+x^3+2 x^5)}{x^6 (-1+x^3+x^5)} \, dx\) [1511]
3.16.12
\(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (-2+x^3+x^6)}{x^9} \, dx\) [1512]
3.16.13
\(\int \genfrac {}{}{}{}{(-1+x^6)^{2/3} (1+x^6) (-1-x^3+x^6)}{x^6 (-1+x^3+x^6)} \, dx\) [1513]
3.16.14
\(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-2+2 x^3+x^6)}{x^9} \, dx\) [1514]
3.16.15
\(\int \genfrac {}{}{}{}{-2+x^4}{\sqrt [4]{1+x^4} (-2+x^4+x^8)} \, dx\) [1515]
3.16.16
\(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (2+x^4)}{x^2 (2+2 x^4+x^8)} \, dx\) [1516]
3.16.17
\(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (2+x^4)}{x^2 (2+2 x^4+x^8)} \, dx\) [1517]
3.16.18
\(\int \genfrac {}{}{}{}{-2 b-2 a x^4+x^8}{x^4 \sqrt [4]{b+a x^4}} \, dx\) [1518]
3.16.19
\(\int \genfrac {}{}{}{}{1-2 x^4+2 x^8}{\sqrt [4]{1+x^4} (-2-x^4+x^8)} \, dx\) [1519]
3.16.20
\(\int \genfrac {}{}{}{}{(1+x^3+x^8)^{2/3} (-3+5 x^8)}{x^3 (1+x^8)} \, dx\) [1520]
3.16.21
\(\int \genfrac {}{}{}{}{-b+2 a x^8}{\sqrt [4]{b+a x^4} (-b+a x^8)} \, dx\) [1521]
3.16.22
\(\int \genfrac {}{}{}{}{\sqrt {-1-x^2+x^6} (1+2 x^6)}{8-x^4-16 x^6+8 x^{12}} \, dx\) [1522]
3.16.23
\(\int \genfrac {}{}{}{}{1}{(1+x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\) [1523]
3.16.24
\(\int \genfrac {}{}{}{}{\sqrt {x-\sqrt {1+x^2}}}{x^2+\sqrt {1+x^2}} \, dx\) [1524]
3.16.25
\(\int \genfrac {}{}{}{}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{x^2} \, dx\) [1525]
3.16.26
\(\int \genfrac {}{}{}{}{-1+x}{(1+x) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [1526]
3.16.27
\(\int \genfrac {}{}{}{}{1}{(-2+x) \sqrt [3]{1+2 x+x^2}} \, dx\) [1527]
3.16.28
\(\int \genfrac {}{}{}{}{\sqrt [3]{-x+x^3}}{x^2} \, dx\) [1528]
3.16.29
\(\int \genfrac {}{}{}{}{\sqrt [3]{-x^2+x^3}}{x} \, dx\) [1529]
3.16.30
\(\int \genfrac {}{}{}{}{-3 b+a x^2}{(-b+a x^2+x^3) \sqrt [4]{-b x+a x^3}} \, dx\) [1530]
3.16.31
\(\int \genfrac {}{}{}{}{1}{(-2 b+a x) \sqrt [4]{-b x^2+a x^3}} \, dx\) [1531]
3.16.32
\(\int \genfrac {}{}{}{}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1532]
3.16.33
\(\int \genfrac {}{}{}{}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1533]
3.16.34
\(\int \genfrac {}{}{}{}{-b+a x^2}{(b-a x^2+x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1534]
3.16.35
\(\int \genfrac {}{}{}{}{-b+a x^2}{(b-a x^2+x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1535]
3.16.36
\(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1536]
3.16.37
\(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1537]
3.16.38
\(\int \genfrac {}{}{}{}{b^3+a^3 x^3}{(-b^3+a^3 x^3) \sqrt {b^4+a^4 x^4}} \, dx\) [1538]
3.16.39
\(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1+x^3+2 x^6)}{x^6 (-1+2 x^6)} \, dx\) [1539]
3.16.40
\(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1+x^3+2 x^6)}{x^6 (-1+2 x^6)} \, dx\) [1540]
3.16.41
\(\int \genfrac {}{}{}{}{(1+x^6) (-1+2 x^6) (-1+x^4+2 x^6)^{5/4}}{x^{10} (-1-x^4+2 x^6)} \, dx\) [1541]
3.16.42
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+a^6 x^6)} \, dx\) [1542]
3.16.43
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+a^6 x^6)} \, dx\) [1543]
3.16.44
\(\int \genfrac {}{}{}{}{((1-3 k^2) x+2 k^2 x^3) (1-2 k^2 x^2+k^4 x^4)}{((1-x^2) (1-k^2 x^2))^{3/4} (1-d+(-1+3 d k^2) x^2-3 d k^4 x^4+d k^6 x^6)} \, dx\) [1544]
3.16.45
\(\int \genfrac {}{}{}{}{\sqrt [4]{-1+2 x^4} (-1+x^4+x^8)}{x^6 (-1+x^4)} \, dx\) [1545]
3.16.46
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\) [1546]
3.16.47
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\) [1547]
3.16.48
\(\int x^6 (-1+x^3)^{2/3} \, dx\) [1548]
3.16.49
\(\int x^6 (1+x^3)^{2/3} \, dx\) [1549]
3.16.50
\(\int x^4 \sqrt [3]{x+x^3} \, dx\) [1550]
3.16.51
\(\int \genfrac {}{}{}{}{x^2 (3 a b^2-2 b (2 a+b) x+(a+2 b) x^2)}{(x (-a+x) (-b+x)^2)^{3/4} (a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3)} \, dx\) [1551]
3.16.52
\(\int \genfrac {}{}{}{}{\sqrt [3]{1+x^4} (3+x^4)}{x^{17}} \, dx\) [1552]
3.16.53
\(\int \genfrac {}{}{}{}{(-2+x^2) \sqrt [3]{x+x^3}}{x^2 (4-2 x^2+x^4)} \, dx\) [1553]
3.16.54
\(\int \genfrac {}{}{}{}{(-2+x^2) \sqrt [3]{x+x^3}}{x^2 (4-2 x^2+x^4)} \, dx\) [1554]
3.16.55
\(\int \genfrac {}{}{}{}{1}{(-1+x^4)^2 \sqrt [4]{-x^2+x^4}} \, dx\) [1555]
3.16.56
\(\int \genfrac {}{}{}{}{(-1+x^2) (1-x+x^2-x^3+x^4)}{(1-x+x^2)^2 (1+x+x^2) \sqrt {1+3 x^2+x^4}} \, dx\) [1556]
3.16.57
\(\int \genfrac {}{}{}{}{(b+a x^3) (b+2 a x^3)}{x^6 \sqrt [4]{b x+a x^4}} \, dx\) [1557]
3.16.58
\(\int \genfrac {}{}{}{}{-b^3+a^3 x^3}{(b^3+a^3 x^3) \sqrt {b^4+a^4 x^4}} \, dx\) [1558]
3.16.59
\(\int \genfrac {}{}{}{}{x^4 (-2 b+a x^2)}{(-b+a x^2)^2 \sqrt [4]{-b+a x^2+c x^4}} \, dx\) [1559]
3.16.60
\(\int \genfrac {}{}{}{}{(-1-2 x+x^2) (-1+2 x+x^2)}{(1-x+2 x^2+x^3+x^4) \sqrt [3]{-x+x^5}} \, dx\) [1560]
3.16.61
\(\int \genfrac {}{}{}{}{-b-a x^3+x^6}{x^6 \sqrt [4]{b x+a x^4}} \, dx\) [1561]
3.16.62
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+a^6 x^6)} \, dx\) [1562]
3.16.63
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+a^6 x^6)} \, dx\) [1563]
3.16.64
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+2 a^6 x^6)} \, dx\) [1564]
3.16.65
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+2 a^6 x^6)} \, dx\) [1565]
3.16.66
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+2 a^6 x^6)} \, dx\) [1566]
3.16.67
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+2 a^6 x^6)} \, dx\) [1567]
3.16.68
\(\int \genfrac {}{}{}{}{x^4 (-4+x^3)}{\sqrt [4]{-1+x^3} (-1+2 x^3-x^6+x^8)} \, dx\) [1568]
3.16.69
\(\int \genfrac {}{}{}{}{x^6}{(b+a x^4)^{3/4} (-b^2+a^2 x^8)} \, dx\) [1569]
3.16.70
\(\int \genfrac {}{}{}{}{(-b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}}{b^2+a x^2} \, dx\) [1570]
3.16.71
\(\int \sqrt [3]{x^2+x^3} \, dx\) [1571]
3.16.72
\(\int \genfrac {}{}{}{}{-1+k^3 x^3}{\sqrt {(1-x) x (1-k^2 x)} (1+k^3 x^3)} \, dx\) [1572]
3.16.73
\(\int \genfrac {}{}{}{}{b+a x^2}{(b+a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1573]
3.16.74
\(\int \genfrac {}{}{}{}{b+a x^2}{(b+a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1574]
3.16.75
\(\int \genfrac {}{}{}{}{c+b x^2+c k^2 x^4}{\sqrt {(1-x^2) (1-k^2 x^2)} (-1+k^2 x^4)} \, dx\) [1575]
3.16.76
\(\int \genfrac {}{}{}{}{3 b+a x^4}{(-b+x^3+a x^4) \sqrt [4]{-b x+a x^5}} \, dx\) [1576]
3.16.77
\(\int \genfrac {}{}{}{}{-1+x^6}{x^6 \sqrt [3]{x+x^3}} \, dx\) [1577]
3.16.78
\(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (2+x^6)}{x^6} \, dx\) [1578]
3.16.79
\(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-2+x^3+x^6)}{x^6} \, dx\) [1579]
3.16.80
\(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1+2 x^6)}{x^6} \, dx\) [1580]
3.16.81
\(\int \genfrac {}{}{}{}{3 b+2 a x^5}{(-b+x^3+a x^5) \sqrt [4]{-b x+a x^6}} \, dx\) [1581]
3.16.82
\(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (1+x^4+x^8)}{x^6 (-1+2 x^8)} \, dx\) [1582]
3.16.83
\(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (1+x^4+x^8)}{x^6 (-1+2 x^8)} \, dx\) [1583]
3.16.84
\(\int \genfrac {}{}{}{}{\sqrt {-b x+a^2 x^2}}{(a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\) [1584]
3.16.85
\(\int x^7 \sqrt [3]{-1+x^3} \, dx\) [1585]
3.16.86
\(\int x^7 \sqrt [3]{1+x^3} \, dx\) [1586]
3.16.87
\(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^3} (1+x^3)}{x^{13}} \, dx\) [1587]
3.16.88
\(\int \genfrac {}{}{}{}{(-b+x) (a-3 b+2 x)}{(-a+x) ((-a+x) (-b+x))^{3/4} (b-a^3 d-(1-3 a^2 d) x-3 a d x^2+d x^3)} \, dx\) [1588]
3.16.89
\(\int x^8 (-b+a x^4)^{3/4} \, dx\) [1589]
3.16.90
\(\int \genfrac {}{}{}{}{1}{(b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\) [1590]
3.16.91
\(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1591]
3.16.92
\(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1592]
3.16.93
\(\int \genfrac {}{}{}{}{(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{\sqrt [3]{(1-x) x (1-k x)} (1-2 (1+k) x+(1+c+4 k+k^2) x^2-(c+2 k+c k+2 k^2) x^3+(-b+c k+k^2) x^4)} \, dx\) [1593]
3.16.94
\(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^6} (1+x^6)}{x^3} \, dx\) [1594]
3.16.95
\(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1-2 x^3+x^6)}{x^6 (-2+x^6)} \, dx\) [1595]
3.16.96
\(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1-2 x^3+x^6)}{x^6 (-2+x^6)} \, dx\) [1596]
3.16.97
\(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^6} (-1+2 x^6)}{x^9} \, dx\) [1597]
3.16.98
\(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-1+x^6)}{x^6 (-2+x^3+2 x^6)} \, dx\) [1598]
3.16.99
\(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-1+x^6)}{x^6 (-2+x^3+2 x^6)} \, dx\) [1599]
3.16.100
\(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (2-x^4+2 x^8)}{x^{10} (-1+2 x^4)} \, dx\) [1600]
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