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3.6
Integrals 501 to 600
\(\int (a+x^2)^{5/2} (x-\sqrt {a+x^2})^n \, dx\) [501]
\(\int (a+x^2)^{3/2} (x-\sqrt {a+x^2})^n \, dx\) [502]
\(\int \sqrt {a+x^2} (x-\sqrt {a+x^2})^n \, dx\) [503]
\(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{\sqrt {a+x^2}} \, dx\) [504]
\(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{(a+x^2)^{3/2}} \, dx\) [505]
\(\int \genfrac {}{}{}{}{(x-\sqrt {a+x^2})^n}{(a+x^2)^{5/2}} \, dx\) [506]
\(\int (a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^2 (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [507]
\(\int (a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}) (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [508]
\(\int (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [509]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}} \, dx\) [510]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{(a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^2} \, dx\) [511]
\(\int (d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n \, dx\) [512]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n}{a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}} \, dx\) [513]
\(\int (a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^{3/2} (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [514]
\(\int \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}} (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [515]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{\sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}}} \, dx\) [516]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{(a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2})^{3/2}} \, dx\) [517]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}}} \, dx\) [518]
\(\int \sqrt {a g+\genfrac {}{}{}{}{2 d e g x}{f^2}+\genfrac {}{}{}{}{e^2 g x^2}{f^2}} (d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n \, dx\) [519]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{\sqrt {a g+\genfrac {}{}{}{}{2 d e g x}{f^2}+\genfrac {}{}{}{}{e^2 g x^2}{f^2}}} \, dx\) [520]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {a+\genfrac {}{}{}{}{2 d e x}{f^2}+\genfrac {}{}{}{}{e^2 x^2}{f^2}})^n}{(a g+\genfrac {}{}{}{}{2 d e g x}{f^2}+\genfrac {}{}{}{}{e^2 g x^2}{f^2})^{3/2}} \, dx\) [521]
\(\int \genfrac {}{}{}{}{(d+e x+f \sqrt {\genfrac {}{}{}{}{a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt {\genfrac {}{}{}{}{a f^2 g+e g x (2 d+e x)}{f^2}}} \, dx\) [522]
\(\int \genfrac {}{}{}{}{1}{(a+b x) \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [523]
\(\int \genfrac {}{}{}{}{e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\) [524]
\(\int \genfrac {}{}{}{}{e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\) [525]
\(\int \genfrac {}{}{}{}{e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\) [526]
\(\int \genfrac {}{}{}{}{e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\) [527]
\(\int \genfrac {}{}{}{}{e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [528]
\(\int \genfrac {}{}{}{}{e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [529]
\(\int \genfrac {}{}{}{}{x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx\) [530]
\(\int \genfrac {}{}{}{}{x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx\) [531]
\(\int \genfrac {}{}{}{}{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx\) [532]
\(\int \genfrac {}{}{}{}{x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx\) [533]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx\) [534]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx\) [535]
\(\int \genfrac {}{}{}{}{x (2 e-2 f x^3)}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx\) [536]
\(\int \genfrac {}{}{}{}{x (2 e-2 f x^3)}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx\) [537]
\(\int \genfrac {}{}{}{}{x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx\) [538]
\(\int \genfrac {}{}{}{}{x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx\) [539]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx\) [540]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx\) [541]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [542]
\(\int \genfrac {}{}{}{}{x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\) [543]
\(\int \genfrac {}{}{}{}{x^5}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [544]
\(\int \genfrac {}{}{}{}{x^3}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [545]
\(\int \genfrac {}{}{}{}{x}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [546]
\(\int \genfrac {}{}{}{}{1}{x (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [547]
\(\int \genfrac {}{}{}{}{1}{x^3 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [548]
\(\int \genfrac {}{}{}{}{x^2}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [549]
\(\int \genfrac {}{}{}{}{1}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\) [550]
\(\int \genfrac {}{}{}{}{1}{x^2 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\) [551]
\(\int \genfrac {}{}{}{}{x^8}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [552]
\(\int \genfrac {}{}{}{}{x^5}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [553]
\(\int \genfrac {}{}{}{}{x^2}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [554]
\(\int \genfrac {}{}{}{}{1}{x (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [555]
\(\int \genfrac {}{}{}{}{1}{x^4 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [556]
\(\int \genfrac {}{}{}{}{x^3}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [557]
\(\int \genfrac {}{}{}{}{x}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [558]
\(\int \genfrac {}{}{}{}{1}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\) [559]
\(\int \genfrac {}{}{}{}{1}{x^2 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [560]
\(\int \genfrac {}{}{}{}{1}{x^3 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\) [561]
\(\int \genfrac {}{}{}{}{1}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [562]
\(\int \genfrac {}{}{}{}{x^m}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [563]
\(\int \genfrac {}{}{}{}{x^{-1+n}}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\) [564]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x}+4 x^{3/2}} \, dx\) [565]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x}-x^{5/2}} \, dx\) [566]
\(\int \genfrac {}{}{}{}{1}{-\sqrt [4]{x}+\sqrt {x}} \, dx\) [567]
\(\int \genfrac {}{}{}{}{1}{\sqrt [3]{x}+\sqrt {x}} \, dx\) [568]
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{x}+\sqrt {x}} \, dx\) [569]
\(\int \genfrac {}{}{}{}{1}{-\sqrt [3]{x}+x^{2/3}} \, dx\) [570]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{1}{\sqrt [4]{x}}+\sqrt {x}} \, dx\) [571]
\(\int \genfrac {}{}{}{}{1}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\) [572]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\genfrac {}{}{}{}{1}{\sqrt [4]{x}}} \, dx\) [573]
\(\int \genfrac {}{}{}{}{1}{-\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\sqrt {x}} \, dx\) [574]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{x+x^2} \, dx\) [575]
\(\int \genfrac {}{}{}{}{x}{4 \sqrt {x}+x} \, dx\) [576]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt [3]{x}+x} \, dx\) [577]
\(\int \genfrac {}{}{}{}{\sqrt [3]{x}}{\sqrt [4]{x}+\sqrt {x}} \, dx\) [578]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\) [579]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{-\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+\sqrt {x}} \, dx\) [580]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}} x^m}{\sqrt {a-b x}} \, dx\) [581]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}} x^2}{\sqrt {a-b x}} \, dx\) [582]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}} x}{\sqrt {a-b x}} \, dx\) [583]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}}}{\sqrt {a-b x}} \, dx\) [584]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}}}{x \sqrt {a-b x}} \, dx\) [585]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x}}}{x^2 \sqrt {a-b x}} \, dx\) [586]
\(\int (a+\genfrac {}{}{}{}{b}{x})^m (c+d x)^n \, dx\) [587]
\(\int (a+\genfrac {}{}{}{}{b}{x})^m (c+d x)^2 \, dx\) [588]
\(\int (a+\genfrac {}{}{}{}{b}{x})^m (c+d x) \, dx\) [589]
\(\int (a+\genfrac {}{}{}{}{b}{x})^m \, dx\) [590]
\(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{c+d x} \, dx\) [591]
\(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{(c+d x)^2} \, dx\) [592]
\(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{(c+d x)^3} \, dx\) [593]
\(\int \genfrac {}{}{}{}{(a+\genfrac {}{}{}{}{b}{x})^m}{(c+d x)^4} \, dx\) [594]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}} x^m}{\sqrt {a-b x^2}} \, dx\) [595]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}} x^2}{\sqrt {a-b x^2}} \, dx\) [596]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}} x}{\sqrt {a-b x^2}} \, dx\) [597]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}}}{\sqrt {a-b x^2}} \, dx\) [598]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}}}{x \sqrt {a-b x^2}} \, dx\) [599]
\(\int \genfrac {}{}{}{}{\sqrt {b-\genfrac {}{}{}{}{a}{x^2}}}{x^2 \sqrt {a-b x^2}} \, dx\) [600]
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