3.16 Integrals 1501 to 1600

   \(\int \genfrac {}{}{}{}{(2+x)^2}{x (4-2 x+x^2) \sqrt [3]{1+x+x^2}} \, dx\) [1501]
   \(\int \genfrac {}{}{}{}{1}{(-2 b+a x^2) \sqrt [4]{-b+a x^2}} \, dx\) [1502]
   \(\int \genfrac {}{}{}{}{-1+x}{x^7 \sqrt [3]{1+x^3}} \, dx\) [1503]
   \(\int \genfrac {}{}{}{}{3 c+2 b x+a x^2}{\sqrt [3]{c+b x+a x^2} (c+b x+a x^2+x^3)} \, dx\) [1504]
   \(\int \genfrac {}{}{}{}{-b+a x^2}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1505]
   \(\int \genfrac {}{}{}{}{-b+a x^2}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1506]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1507]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1508]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1509]
   \(\int \genfrac {}{}{}{}{x (3+5 x^2)}{\sqrt [3]{1+x^2} (-1+x^3+x^5)} \, dx\) [1510]
   \(\int \genfrac {}{}{}{}{(-1+x^5)^{2/3} (3+2 x^5) (-2+x^3+2 x^5)}{x^6 (-1+x^3+x^5)} \, dx\) [1511]
   \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (-2+x^3+x^6)}{x^9} \, dx\) [1512]
   \(\int \genfrac {}{}{}{}{(-1+x^6)^{2/3} (1+x^6) (-1-x^3+x^6)}{x^6 (-1+x^3+x^6)} \, dx\) [1513]
   \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-2+2 x^3+x^6)}{x^9} \, dx\) [1514]
   \(\int \genfrac {}{}{}{}{-2+x^4}{\sqrt [4]{1+x^4} (-2+x^4+x^8)} \, dx\) [1515]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (2+x^4)}{x^2 (2+2 x^4+x^8)} \, dx\) [1516]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (2+x^4)}{x^2 (2+2 x^4+x^8)} \, dx\) [1517]
   \(\int \genfrac {}{}{}{}{-2 b-2 a x^4+x^8}{x^4 \sqrt [4]{b+a x^4}} \, dx\) [1518]
   \(\int \genfrac {}{}{}{}{1-2 x^4+2 x^8}{\sqrt [4]{1+x^4} (-2-x^4+x^8)} \, dx\) [1519]
   \(\int \genfrac {}{}{}{}{(1+x^3+x^8)^{2/3} (-3+5 x^8)}{x^3 (1+x^8)} \, dx\) [1520]
   \(\int \genfrac {}{}{}{}{-b+2 a x^8}{\sqrt [4]{b+a x^4} (-b+a x^8)} \, dx\) [1521]
   \(\int \genfrac {}{}{}{}{\sqrt {-1-x^2+x^6} (1+2 x^6)}{8-x^4-16 x^6+8 x^{12}} \, dx\) [1522]
   \(\int \genfrac {}{}{}{}{1}{(1+x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\) [1523]
   \(\int \genfrac {}{}{}{}{\sqrt {x-\sqrt {1+x^2}}}{x^2+\sqrt {1+x^2}} \, dx\) [1524]
   \(\int \genfrac {}{}{}{}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{x^2} \, dx\) [1525]
   \(\int \genfrac {}{}{}{}{-1+x}{(1+x) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\) [1526]
   \(\int \genfrac {}{}{}{}{1}{(-2+x) \sqrt [3]{1+2 x+x^2}} \, dx\) [1527]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-x+x^3}}{x^2} \, dx\) [1528]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-x^2+x^3}}{x} \, dx\) [1529]
   \(\int \genfrac {}{}{}{}{-3 b+a x^2}{(-b+a x^2+x^3) \sqrt [4]{-b x+a x^3}} \, dx\) [1530]
   \(\int \genfrac {}{}{}{}{1}{(-2 b+a x) \sqrt [4]{-b x^2+a x^3}} \, dx\) [1531]
   \(\int \genfrac {}{}{}{}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1532]
   \(\int \genfrac {}{}{}{}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}}{x^4 (b+a x^4)} \, dx\) [1533]
   \(\int \genfrac {}{}{}{}{-b+a x^2}{(b-a x^2+x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1534]
   \(\int \genfrac {}{}{}{}{-b+a x^2}{(b-a x^2+x^4) \sqrt [4]{b x^2+a x^4}} \, dx\) [1535]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1536]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1537]
   \(\int \genfrac {}{}{}{}{b^3+a^3 x^3}{(-b^3+a^3 x^3) \sqrt {b^4+a^4 x^4}} \, dx\) [1538]
   \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1+x^3+2 x^6)}{x^6 (-1+2 x^6)} \, dx\) [1539]
   \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1+x^3+2 x^6)}{x^6 (-1+2 x^6)} \, dx\) [1540]
   \(\int \genfrac {}{}{}{}{(1+x^6) (-1+2 x^6) (-1+x^4+2 x^6)^{5/4}}{x^{10} (-1-x^4+2 x^6)} \, dx\) [1541]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+a^6 x^6)} \, dx\) [1542]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+a^6 x^6)} \, dx\) [1543]
   \(\int \genfrac {}{}{}{}{((1-3 k^2) x+2 k^2 x^3) (1-2 k^2 x^2+k^4 x^4)}{((1-x^2) (1-k^2 x^2))^{3/4} (1-d+(-1+3 d k^2) x^2-3 d k^4 x^4+d k^6 x^6)} \, dx\) [1544]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-1+2 x^4} (-1+x^4+x^8)}{x^6 (-1+x^4)} \, dx\) [1545]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\) [1546]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\) [1547]
   \(\int x^6 (-1+x^3)^{2/3} \, dx\) [1548]
   \(\int x^6 (1+x^3)^{2/3} \, dx\) [1549]
   \(\int x^4 \sqrt [3]{x+x^3} \, dx\) [1550]
   \(\int \genfrac {}{}{}{}{x^2 (3 a b^2-2 b (2 a+b) x+(a+2 b) x^2)}{(x (-a+x) (-b+x)^2)^{3/4} (a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3)} \, dx\) [1551]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{1+x^4} (3+x^4)}{x^{17}} \, dx\) [1552]
   \(\int \genfrac {}{}{}{}{(-2+x^2) \sqrt [3]{x+x^3}}{x^2 (4-2 x^2+x^4)} \, dx\) [1553]
   \(\int \genfrac {}{}{}{}{(-2+x^2) \sqrt [3]{x+x^3}}{x^2 (4-2 x^2+x^4)} \, dx\) [1554]
   \(\int \genfrac {}{}{}{}{1}{(-1+x^4)^2 \sqrt [4]{-x^2+x^4}} \, dx\) [1555]
   \(\int \genfrac {}{}{}{}{(-1+x^2) (1-x+x^2-x^3+x^4)}{(1-x+x^2)^2 (1+x+x^2) \sqrt {1+3 x^2+x^4}} \, dx\) [1556]
   \(\int \genfrac {}{}{}{}{(b+a x^3) (b+2 a x^3)}{x^6 \sqrt [4]{b x+a x^4}} \, dx\) [1557]
   \(\int \genfrac {}{}{}{}{-b^3+a^3 x^3}{(b^3+a^3 x^3) \sqrt {b^4+a^4 x^4}} \, dx\) [1558]
   \(\int \genfrac {}{}{}{}{x^4 (-2 b+a x^2)}{(-b+a x^2)^2 \sqrt [4]{-b+a x^2+c x^4}} \, dx\) [1559]
   \(\int \genfrac {}{}{}{}{(-1-2 x+x^2) (-1+2 x+x^2)}{(1-x+2 x^2+x^3+x^4) \sqrt [3]{-x+x^5}} \, dx\) [1560]
   \(\int \genfrac {}{}{}{}{-b-a x^3+x^6}{x^6 \sqrt [4]{b x+a x^4}} \, dx\) [1561]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+a^6 x^6)} \, dx\) [1562]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+a^6 x^6)} \, dx\) [1563]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+2 a^6 x^6)} \, dx\) [1564]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-b+2 a^6 x^6)} \, dx\) [1565]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+2 a^6 x^6)} \, dx\) [1566]
   \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{b^2 x^2+a^3 x^3} (b+2 a^6 x^6)} \, dx\) [1567]
   \(\int \genfrac {}{}{}{}{x^4 (-4+x^3)}{\sqrt [4]{-1+x^3} (-1+2 x^3-x^6+x^8)} \, dx\) [1568]
   \(\int \genfrac {}{}{}{}{x^6}{(b+a x^4)^{3/4} (-b^2+a^2 x^8)} \, dx\) [1569]
   \(\int \genfrac {}{}{}{}{(-b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}}{b^2+a x^2} \, dx\) [1570]
   \(\int \sqrt [3]{x^2+x^3} \, dx\) [1571]
   \(\int \genfrac {}{}{}{}{-1+k^3 x^3}{\sqrt {(1-x) x (1-k^2 x)} (1+k^3 x^3)} \, dx\) [1572]
   \(\int \genfrac {}{}{}{}{b+a x^2}{(b+a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1573]
   \(\int \genfrac {}{}{}{}{b+a x^2}{(b+a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\) [1574]
   \(\int \genfrac {}{}{}{}{c+b x^2+c k^2 x^4}{\sqrt {(1-x^2) (1-k^2 x^2)} (-1+k^2 x^4)} \, dx\) [1575]
   \(\int \genfrac {}{}{}{}{3 b+a x^4}{(-b+x^3+a x^4) \sqrt [4]{-b x+a x^5}} \, dx\) [1576]
   \(\int \genfrac {}{}{}{}{-1+x^6}{x^6 \sqrt [3]{x+x^3}} \, dx\) [1577]
   \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (2+x^6)}{x^6} \, dx\) [1578]
   \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-2+x^3+x^6)}{x^6} \, dx\) [1579]
   \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1+2 x^6)}{x^6} \, dx\) [1580]
   \(\int \genfrac {}{}{}{}{3 b+2 a x^5}{(-b+x^3+a x^5) \sqrt [4]{-b x+a x^6}} \, dx\) [1581]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (1+x^4+x^8)}{x^6 (-1+2 x^8)} \, dx\) [1582]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (1+x^4+x^8)}{x^6 (-1+2 x^8)} \, dx\) [1583]
   \(\int \genfrac {}{}{}{}{\sqrt {-b x+a^2 x^2}}{(a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\) [1584]
   \(\int x^7 \sqrt [3]{-1+x^3} \, dx\) [1585]
   \(\int x^7 \sqrt [3]{1+x^3} \, dx\) [1586]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^3} (1+x^3)}{x^{13}} \, dx\) [1587]
   \(\int \genfrac {}{}{}{}{(-b+x) (a-3 b+2 x)}{(-a+x) ((-a+x) (-b+x))^{3/4} (b-a^3 d-(1-3 a^2 d) x-3 a d x^2+d x^3)} \, dx\) [1588]
   \(\int x^8 (-b+a x^4)^{3/4} \, dx\) [1589]
   \(\int \genfrac {}{}{}{}{1}{(b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\) [1590]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1591]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-b x^2+a x^4}}{x^4 (-b+a x^4)} \, dx\) [1592]
   \(\int \genfrac {}{}{}{}{(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{\sqrt [3]{(1-x) x (1-k x)} (1-2 (1+k) x+(1+c+4 k+k^2) x^2-(c+2 k+c k+2 k^2) x^3+(-b+c k+k^2) x^4)} \, dx\) [1593]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^6} (1+x^6)}{x^3} \, dx\) [1594]
   \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1-2 x^3+x^6)}{x^6 (-2+x^6)} \, dx\) [1595]
   \(\int \genfrac {}{}{}{}{(1+x^3)^{2/3} (1-2 x^3+x^6)}{x^6 (-2+x^6)} \, dx\) [1596]
   \(\int \genfrac {}{}{}{}{\sqrt [3]{-1+x^6} (-1+2 x^6)}{x^9} \, dx\) [1597]
   \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-1+x^6)}{x^6 (-2+x^3+2 x^6)} \, dx\) [1598]
   \(\int \genfrac {}{}{}{}{(-1+x^3)^{2/3} (-1+x^6)}{x^6 (-2+x^3+2 x^6)} \, dx\) [1599]
   \(\int \genfrac {}{}{}{}{\sqrt [4]{-1+x^4} (2-x^4+2 x^8)}{x^{10} (-1+2 x^4)} \, dx\) [1600]