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3.6
Integrals 501 to 600
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]
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