3.6.1 \(\int (a+x^2)^{5/2} (x-\sqrt {a+x^2})^n \, dx\) [501]
3.6.2 \(\int (a+x^2)^{3/2} (x-\sqrt {a+x^2})^n \, dx\) [502]
3.6.3 \(\int \sqrt {a+x^2} (x-\sqrt {a+x^2})^n \, dx\) [503]
3.6.4 \(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{\sqrt {a+x^2}} \, dx\) [504]
3.6.5 \(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{(a+x^2)^{3/2}} \, dx\) [505]
3.6.6 \(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{(a+x^2)^{5/2}} \, dx\) [506]
3.6.7 \(\int (a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^2 (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [507]
3.6.8 \(\int (a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}) (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [508]
3.6.9 \(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [509]
3.6.10 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}} \, dx\) [510]
3.6.11 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{(a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^2} \, dx\) [511]
3.6.12 \(\int (d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n \, dx\) [512]
3.6.13 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n}{a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}} \, dx\) [513]
3.6.14 \(\int (a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^{3/2} (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [514]
3.6.15 \(\int \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}} (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [515]
3.6.16 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{\sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}}} \, dx\) [516]
3.6.17 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{(a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^{3/2}} \, dx\) [517]
3.6.18 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}}} \, dx\) [518]
3.6.19 \(\int \sqrt {a g+\genfrac {}{}{}{}{2 d e g x}{f^2}+\genfrac {}{}{}{}{e^2 g x^2}{f^2}} (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [519]
3.6.20 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{\sqrt {a g+\genfrac {}{}{}{}{2 d e g x}{f^2}+\genfrac {}{}{}{}{e^2 g x^2}{f^2}}} \, dx\) [520]
3.6.21 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{(a g+\genfrac {}{}{}{}{2 d e g x}{f^2}+\genfrac {}{}{}{}{e^2 g x^2}{f^2})^{3/2}} \, dx\) [521]
3.6.22 \(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt {\genfrac {}{}{}{}{a f^2 g+e g x (2 d+e x)}{f^2}}} \, dx\) [522]
3.6.23 \(\int \genfrac {}{}{}{}{1}{(a+b x) \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [523]
3.6.24 \(\int \genfrac {}{}{}{}{e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\) [524]
3.6.25 \(\int \genfrac {}{}{}{}{e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\) [525]
3.6.26 \(\int \genfrac {}{}{}{}{e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\) [526]
3.6.27 \(\int \genfrac {}{}{}{}{e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\) [527]
3.6.28 \(\int \genfrac {}{}{}{}{e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [528]
3.6.29 \(\int \genfrac {}{}{}{}{e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [529]
3.6.30 \(\int \genfrac {}{}{}{}{x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx\) [530]
3.6.31 \(\int \genfrac {}{}{}{}{x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx\) [531]
3.6.32 \(\int \genfrac {}{}{}{}{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx\) [532]
3.6.33 \(\int \genfrac {}{}{}{}{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx\) [533]
3.6.34 \(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx\) [534]
3.6.35 \(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx\) [535]
3.6.36 \(\int \genfrac {}{}{}{}{x (2 e-2 f x^3)}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx\) [536]
3.6.37 \(\int \genfrac {}{}{}{}{x (2 e-2 f x^3)}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx\) [537]
3.6.38 \(\int \genfrac {}{}{}{}{x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx\) [538]
3.6.39 \(\int \genfrac {}{}{}{}{x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx\) [539]
3.6.40 \(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx\) [540]
3.6.41 \(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx\) [541]
3.6.42 \(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [542]
3.6.43 \(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [543]
3.6.44 \(\int \genfrac {}{}{}{}{x^5}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [544]
3.6.45 \(\int \genfrac {}{}{}{}{x^3}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [545]
3.6.46 \(\int \genfrac {}{}{}{}{x}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [546]
3.6.47 \(\int \genfrac {}{}{}{}{1}{x (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [547]
3.6.48 \(\int \genfrac {}{}{}{}{1}{x^3 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [548]
3.6.49 \(\int \genfrac {}{}{}{}{x^2}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [549]
3.6.50 \(\int \genfrac {}{}{}{}{1}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [550]
3.6.51 \(\int \genfrac {}{}{}{}{1}{x^2 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [551]
3.6.52 \(\int \genfrac {}{}{}{}{x^8}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [552]
3.6.53 \(\int \genfrac {}{}{}{}{x^5}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [553]
3.6.54 \(\int \genfrac {}{}{}{}{x^2}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [554]
3.6.55 \(\int \genfrac {}{}{}{}{1}{x (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [555]
3.6.56 \(\int \genfrac {}{}{}{}{1}{x^4 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [556]
3.6.57 \(\int \genfrac {}{}{}{}{x^3}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [557]
3.6.58 \(\int \genfrac {}{}{}{}{x}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [558]
3.6.59 \(\int \genfrac {}{}{}{}{1}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [559]
3.6.60 \(\int \genfrac {}{}{}{}{1}{x^2 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [560]
3.6.61 \(\int \genfrac {}{}{}{}{1}{x^3 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [561]
3.6.62 \(\int \genfrac {}{}{}{}{1}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [562]
3.6.63 \(\int \genfrac {}{}{}{}{x^m}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [563]
3.6.64 \(\int \genfrac {}{}{}{}{x^{-1+n}}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [564]
3.6.65 \(\int \genfrac {}{}{}{}{1}{\sqrt {x}+4 x^{3/2}} \, dx\) [565]
3.6.66 \(\int \genfrac {}{}{}{}{1}{\sqrt {x}-x^{5/2}} \, dx\) [566]
3.6.67 \(\int \genfrac {}{}{}{}{1}{-\sqrt [4]{x}+\sqrt {x}} \, dx\) [567]
3.6.68 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{x}+\sqrt {x}} \, dx\) [568]
3.6.69 \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{x}+\sqrt {x}} \, dx\) [569]
3.6.70 \(\int \genfrac {}{}{}{}{1}{-\sqrt [3]{x}+x^{2/3}} \, dx\) [570]
3.6.71 \(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{1}{\sqrt [4]{x}}+\sqrt {x}} \, dx\) [571]
3.6.72 \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\) [572]
3.6.73 \(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\genfrac {}{}{}{}{1}{\sqrt [4]{x}}} \, dx\) [573]
3.6.74 \(\int \genfrac {}{}{}{}{1}{-\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\sqrt {x}} \, dx\) [574]
3.6.75 \(\int \genfrac {}{}{}{}{\sqrt {x}}{x+x^2} \, dx\) [575]
3.6.76 \(\int \genfrac {}{}{}{}{x}{4 \sqrt {x}+x} \, dx\) [576]
3.6.77 \(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt [3]{x}+x} \, dx\) [577]
3.6.78 \(\int \genfrac {}{}{}{}{\sqrt [3]{x}}{\sqrt [4]{x}+\sqrt {x}} \, dx\) [578]
3.6.79 \(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\) [579]
3.6.80 \(\int \genfrac {}{}{}{}{\sqrt {x}}{-\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\sqrt {x}} \, dx\) [580]
3.6.81 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}} x^m}{\sqrt {a-b x}} \, dx\) [581]
3.6.82 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}} x^2}{\sqrt {a-b x}} \, dx\) [582]
3.6.83 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}} x}{\sqrt {a-b x}} \, dx\) [583]
3.6.84 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}}}{\sqrt {a-b x}} \, dx\) [584]
3.6.85 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}}}{x \sqrt {a-b x}} \, dx\) [585]
3.6.86 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}}}{x^2 \sqrt {a-b x}} \, dx\) [586]
3.6.87 \(\int (a+\genfrac {}{}{}{}{b}{x})^m (c+d x)^n \, dx\) [587]
3.6.88 \(\int (a+\genfrac {}{}{}{}{b}{x})^m (c+d x)^2 \, dx\) [588]
3.6.89 \(\int (a+\genfrac {}{}{}{}{b}{x})^m (c+d x) \, dx\) [589]
3.6.90 \(\int (a+\genfrac {}{}{}{}{b}{x})^m \, dx\) [590]
3.6.91 \(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{c+d x} \, dx\) [591]
3.6.92 \(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{(c+d x)^2} \, dx\) [592]
3.6.93 \(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{(c+d x)^3} \, dx\) [593]
3.6.94 \(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{(c+d x)^4} \, dx\) [594]
3.6.95 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}} x^m}{\sqrt {a-b x^2}} \, dx\) [595]
3.6.96 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}} x^2}{\sqrt {a-b x^2}} \, dx\) [596]
3.6.97 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}} x}{\sqrt {a-b x^2}} \, dx\) [597]
3.6.98 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}}}{\sqrt {a-b x^2}} \, dx\) [598]
3.6.99 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}}}{x \sqrt {a-b x^2}} \, dx\) [599]
3.6.100 \(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}}}{x^2 \sqrt {a-b x^2}} \, dx\) [600]