3.15.1 \(\int \genfrac {}{}{}{}{-b+2 a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\) [1401]
3.15.2 \(\int \genfrac {}{}{}{}{(-1+3 x^4) \sqrt {1+x+2 x^4+x^5+x^8}}{x^2 (4+x+4 x^4)} \, dx\) [1402]
3.15.3 \(\int \genfrac {}{}{}{}{-b+c x^4+a x^8}{x^2 (-b+a x^4)^{3/4}} \, dx\) [1403]
3.15.4 \(\int \genfrac {}{}{}{}{1}{(1+x) \sqrt {x+\sqrt {1+x^2}}} \, dx\) [1404]
3.15.5 \(\int \genfrac {}{}{}{}{1}{x \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [1405]
3.15.6 \(\int \genfrac {}{}{}{}{(-3+x)^6 (-1-x+x^2)^{3/2}}{-1+x} \, dx\) [1406]
3.15.7 \(\int \genfrac {}{}{}{}{(-1+x^3) \sqrt [3]{1+x^3}}{x^5} \, dx\) [1407]
3.15.8 \(\int \genfrac {}{}{}{}{(-1+x^3) \sqrt [3]{1+x^3}}{x^2} \, dx\) [1408]
3.15.9 \(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^3} (1+x^3)}{x^5} \, dx\) [1409]
3.15.10 \(\int \genfrac {}{}{}{}{x}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\) [1410]
3.15.11 \(\int \genfrac {}{}{}{}{-1+x+x^2}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\) [1411]
3.15.12 \(\int \genfrac {}{}{}{}{x}{\sqrt [3]{x^2+x^3}} \, dx\) [1412]
3.15.13 \(\int \genfrac {}{}{}{}{1}{x^6 (1+x^3) \sqrt [3]{x^2+x^3}} \, dx\) [1413]
3.15.14 \(\int \genfrac {}{}{}{}{1}{x^6 (1+x^3) \sqrt [3]{x^2+x^3}} \, dx\) [1414]
3.15.15 \(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^5} \, dx\) [1415]
3.15.16 \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-1+3 x^3)}{x^6 (-1+2 x^3)} \, dx\) [1416]
3.15.17 \(\int \genfrac {}{}{}{}{x^4}{(-1+x^4)^2 \sqrt [4]{x^2+x^4}} \, dx\) [1417]
3.15.18 \(\int \genfrac {}{}{}{}{(1+x^2) \sqrt [4]{x^3+x^4}}{x^2 (-1+x^2)} \, dx\) [1418]
3.15.19 \(\int \genfrac {}{}{}{}{(4+x^3) (-1-x^3+x^4)}{x^2 (1+x^3)^{3/4} (1+x^3+x^4)} \, dx\) [1419]
3.15.20 \(\int \genfrac {}{}{}{}{1+x^2+2 x^4}{\sqrt [4]{1+x^2} (2+3 x^2+x^4)} \, dx\) [1420]
3.15.21 \(\int \genfrac {}{}{}{}{(-b+a x^2) \sqrt [4]{-b x^2+a x^4}}{x^2} \, dx\) [1421]
3.15.22 \(\int \genfrac {}{}{}{}{b+a x^4}{x^4 (2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1422]
3.15.23 \(\int \genfrac {}{}{}{}{b+a x^4}{x^4 (2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1423]
3.15.24 \(\int \genfrac {}{}{}{}{1-x^4}{x^2 \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\) [1424]
3.15.25 \(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt [4]{x^2+x^6}} \, dx\) [1425]
3.15.26 \(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt [4]{x^2+x^6}} \, dx\) [1426]
3.15.27 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^3+x^4} (-1+x^8)}{x^4} \, dx\) [1427]
3.15.28 \(\int \genfrac {}{}{}{}{\sqrt [4]{1+x^4} (2+x^4)}{x^2 (-1+2 x^4+x^8)} \, dx\) [1428]
3.15.29 \(\int \genfrac {}{}{}{}{\sqrt [4]{1+x^4} (2+x^4)}{x^2 (-1+2 x^4+x^8)} \, dx\) [1429]
3.15.30 \(\int \genfrac {}{}{}{}{-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-b+a x^8)} \, dx\) [1430]
3.15.31 \(\int \genfrac {}{}{}{}{\sqrt {1+2 x^6} (-1+4 x^6)}{2+x^4+8 x^6+8 x^{12}} \, dx\) [1431]
3.15.32 \(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {1+\sqrt {1+x}}}{1+x^2} \, dx\) [1432]
3.15.33 \(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {1+\sqrt {1+x}}}{1+x^2} \, dx\) [1433]
3.15.34 \(\int x^2 \sqrt {x^2+\sqrt {1+x^4}} \, dx\) [1434]
3.15.35 \(\int \genfrac {}{}{}{}{(-1+x^4) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\) [1435]
3.15.36 \(\int \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}} \, dx\) [1436]
3.15.37 \(\int x^3 (-1+x^3)^{2/3} \, dx\) [1437]
3.15.38 \(\int x^4 \sqrt [3]{1+x^3} \, dx\) [1438]
3.15.39 \(\int x^3 (1+x^3)^{2/3} \, dx\) [1439]
3.15.40 \(\int \genfrac {}{}{}{}{(-2+x^3)^{2/3} (4+x^3)}{x^6 (-1+x^3)} \, dx\) [1440]
3.15.41 \(\int \genfrac {}{}{}{}{3 b+a x^2}{(b+a x^2+x^3) \sqrt [4]{b x+a x^3}} \, dx\) [1441]
3.15.42 \(\int \genfrac {}{}{}{}{(-3+x^4) \sqrt [3]{1+x^4}}{x^{13}} \, dx\) [1442]
3.15.43 \(\int \genfrac {}{}{}{}{-2 b+a x^2}{\sqrt [4]{-b+a x^2} (-b+a x^2+x^4)} \, dx\) [1443]
3.15.44 \(\int \genfrac {}{}{}{}{-4 b+a x^3}{\sqrt [4]{-b+a x^3} (-b+a x^3+x^4)} \, dx\) [1444]
3.15.45 \(\int \genfrac {}{}{}{}{b+a x^2}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1445]
3.15.46 \(\int \genfrac {}{}{}{}{b+a x^2}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1446]
3.15.47 \(\int \genfrac {}{}{}{}{b+a x^4}{x^4 (-2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1447]
3.15.48 \(\int \genfrac {}{}{}{}{b+a x^4}{x^4 (-2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1448]
3.15.49 \(\int \genfrac {}{}{}{}{(-1+x^3) (1+x^3)^3 (1+x^6)^{2/3}}{x^6 (1-x^3+x^6)} \, dx\) [1449]
3.15.50 \(\int \genfrac {}{}{}{}{(-1+x^6)^{2/3} (1+x^6) (-2+x^3+2 x^6)}{x^6 (-1-x^3+x^6)} \, dx\) [1450]
3.15.51 \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\) [1451]
3.15.52 \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\) [1452]
3.15.53 \(\int \genfrac {}{}{}{}{-b+a x^4}{\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4+2 x^8)} \, dx\) [1453]
3.15.54 \(\int \genfrac {}{}{}{}{-b+a x^4}{\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4+2 x^8)} \, dx\) [1454]
3.15.55 \(\int \genfrac {}{}{}{}{\sqrt {c x^2-x \sqrt {-b x+a x^2}}}{x^3} \, dx\) [1455]
3.15.56 \(\int \genfrac {}{}{}{}{x}{x+\sqrt {x+\sqrt {1+x^2}}} \, dx\) [1456]
3.15.57 \(\int \genfrac {}{}{}{}{x}{x+\sqrt {x+\sqrt {1+x^2}}} \, dx\) [1457]
3.15.58 \(\int \genfrac {}{}{}{}{1+x}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\) [1458]
3.15.59 \(\int \genfrac {}{}{}{}{3+x+x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\) [1459]
3.15.60 \(\int \genfrac {}{}{}{}{3-x+2 x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\) [1460]
3.15.61 \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (1+x^3)}{x^3} \, dx\) [1461]
3.15.62 \(\int x^8 (b+a x^4)^{3/4} \, dx\) [1462]
3.15.63 \(\int \genfrac {}{}{}{}{1}{(-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\) [1463]
3.15.64 \(\int \genfrac {}{}{}{}{(-2+x^3) (1+x^3)^{2/3}}{x^3 (-2+x^3+2 x^6)} \, dx\) [1464]
3.15.65 \(\int \genfrac {}{}{}{}{(-2+x^3) (1+x^3)^{2/3}}{x^3 (-2+x^3+2 x^6)} \, dx\) [1465]
3.15.66 \(\int \genfrac {}{}{}{}{x^2 (-2+x^4)}{\sqrt [3]{-x+x^5} (-1+x^4+x^8)} \, dx\) [1466]
3.15.67 \(\int \genfrac {}{}{}{}{-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\) [1467]
3.15.68 \(\int \genfrac {}{}{}{}{-2 b+a x^4}{\sqrt [4]{b+a x^4} (-2 b+a x^4+x^8)} \, dx\) [1468]
3.15.69 \(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\) [1469]
3.15.70 \(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^3}}{x^{10}} \, dx\) [1470]
3.15.71 \(\int x^4 \sqrt [3]{-1+x^3} \, dx\) [1471]
3.15.72 \(\int \sqrt [3]{-x+x^3} \, dx\) [1472]
3.15.73 \(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^{10}} \, dx\) [1473]
3.15.74 \(\int \genfrac {}{}{}{}{1+k^3 x^3}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^3 x^3)} \, dx\) [1474]
3.15.75 \(\int \genfrac {}{}{}{}{(-3+x^4) (1+x^4)^{2/3} (1+2 x^3+x^4)}{x^6 (1-x^3+x^4)} \, dx\) [1475]
3.15.76 \(\int \genfrac {}{}{}{}{(b+a x^4)^{3/4}}{x^4 (2 b+a x^4)} \, dx\) [1476]
3.15.77 \(\int \genfrac {}{}{}{}{-b+a x^3}{x^3 \sqrt [4]{-b x+a x^4}} \, dx\) [1477]
3.15.78 \(\int \genfrac {}{}{}{}{b+a x^3}{x^3 \sqrt [4]{-b x+a x^4}} \, dx\) [1478]
3.15.79 \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x+a x^4}}{x^2} \, dx\) [1479]
3.15.80 \(\int \genfrac {}{}{}{}{1}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1480]
3.15.81 \(\int \genfrac {}{}{}{}{1}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1481]
3.15.82 \(\int \genfrac {}{}{}{}{-b+a x^4}{x^4 \sqrt [4]{-b+2 a x^4}} \, dx\) [1482]
3.15.83 \(\int \genfrac {}{}{}{}{x^4 (4 b+a x^5)}{(-b+a x^5)^2 \sqrt [4]{-b+c x^4+a x^5}} \, dx\) [1483]
3.15.84 \(\int \genfrac {}{}{}{}{1}{x^{19} \sqrt [3]{-1+x^6}} \, dx\) [1484]
3.15.85 \(\int \genfrac {}{}{}{}{x^7}{\sqrt [3]{-1+x^6}} \, dx\) [1485]
3.15.86 \(\int x^3 \sqrt [3]{-1+x^6} \, dx\) [1486]
3.15.87 \(\int x (-1+x^6)^{2/3} \, dx\) [1487]
3.15.88 \(\int \genfrac {}{}{}{}{x^7}{\sqrt [3]{1+x^6}} \, dx\) [1488]
3.15.89 \(\int x^3 \sqrt [3]{1+x^6} \, dx\) [1489]
3.15.90 \(\int x (1+x^6)^{2/3} \, dx\) [1490]
3.15.91 \(\int \genfrac {}{}{}{}{(1-x^3+x^5) (-3+2 x^5)}{x^3 (1+x^3+x^5) \sqrt [4]{x+x^6}} \, dx\) [1491]
3.15.92 \(\int \genfrac {}{}{}{}{x}{\sqrt [3]{-x^2+x^6}} \, dx\) [1492]
3.15.93 \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (2+x^3)}{x^3 (-4+x^3+x^6)} \, dx\) [1493]
3.15.94 \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (2+x^3)}{x^3 (-4+x^3+x^6)} \, dx\) [1494]
3.15.95 \(\int \genfrac {}{}{}{}{(-3+2 x) (1-x+x^3)^{2/3}}{1-2 x+x^2+2 x^3-2 x^4+2 x^6} \, dx\) [1495]
3.15.96 \(\int \genfrac {}{}{}{}{(-2+x^6) (4+x^6) \sqrt [4]{-2+2 x^4+x^6}}{x^6 (-4-x^4+2 x^6)} \, dx\) [1496]
3.15.97 \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (-1+3 x^6)}{x^9 (1+2 x^3)} \, dx\) [1497]
3.15.98 \(\int \genfrac {}{}{}{}{\sqrt {1-x^4} (1+x^4)}{1-x^4+x^8} \, dx\) [1498]
3.15.99 \(\int \genfrac {}{}{}{}{x^2}{(b+a x^4)^{3/4} (-b^2+a^2 x^8)} \, dx\) [1499]
3.15.100 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {1+x^2}}}{x+\sqrt {1+x^2}} \, dx\) [1500]