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3.6
Integrals 501 to 600
3.6.1
\(\int \genfrac {}{}{}{}{4^x}{\sqrt {a+2^{-x} b}} \, dx\) [501]
3.6.2
\(\int \genfrac {}{}{}{}{2^{2 x}}{\sqrt {a+2^{-x} b}} \, dx\) [502]
3.6.3
\(\int \genfrac {}{}{}{}{4^x}{\sqrt {a-2^{-x} b}} \, dx\) [503]
3.6.4
\(\int \genfrac {}{}{}{}{2^{2 x}}{\sqrt {a-2^{-x} b}} \, dx\) [504]
3.6.5
\(\int \genfrac {}{}{}{}{1}{1+2 e^x+e^{2 x}} \, dx\) [505]
3.6.6
\(\int \genfrac {}{}{}{}{1}{2+3 e^x+e^{2 x}} \, dx\) [506]
3.6.7
\(\int \genfrac {}{}{}{}{1}{-1+e^x+e^{2 x}} \, dx\) [507]
3.6.8
\(\int \genfrac {}{}{}{}{1}{3+3 e^x+e^{2 x}} \, dx\) [508]
3.6.9
\(\int \genfrac {}{}{}{}{1}{a+b e^x+c e^{2 x}} \, dx\) [509]
3.6.10
\(\int \genfrac {}{}{}{}{x}{1+2 e^x+e^{2 x}} \, dx\) [510]
3.6.11
\(\int \genfrac {}{}{}{}{x}{2+3 e^x+e^{2 x}} \, dx\) [511]
3.6.12
\(\int \genfrac {}{}{}{}{x}{-1+e^x+e^{2 x}} \, dx\) [512]
3.6.13
\(\int \genfrac {}{}{}{}{x}{3+3 e^x+e^{2 x}} \, dx\) [513]
3.6.14
\(\int \genfrac {}{}{}{}{x}{a+b e^x+c e^{2 x}} \, dx\) [514]
3.6.15
\(\int \genfrac {}{}{}{}{x^2}{1+2 e^x+e^{2 x}} \, dx\) [515]
3.6.16
\(\int \genfrac {}{}{}{}{x^2}{2+3 e^x+e^{2 x}} \, dx\) [516]
3.6.17
\(\int \genfrac {}{}{}{}{x^2}{-1+e^x+e^{2 x}} \, dx\) [517]
3.6.18
\(\int \genfrac {}{}{}{}{x^2}{3+3 e^x+e^{2 x}} \, dx\) [518]
3.6.19
\(\int \genfrac {}{}{}{}{x^2}{a+b e^x+c e^{2 x}} \, dx\) [519]
3.6.20
\(\int \genfrac {}{}{}{}{1}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx\) [520]
3.6.21
\(\int \genfrac {}{}{}{}{1}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx\) [521]
3.6.22
\(\int \genfrac {}{}{}{}{1}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx\) [522]
3.6.23
\(\int \genfrac {}{}{}{}{x}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx\) [523]
3.6.24
\(\int \genfrac {}{}{}{}{x}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx\) [524]
3.6.25
\(\int \genfrac {}{}{}{}{x^2}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx\) [525]
3.6.26
\(\int \genfrac {}{}{}{}{x^2}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx\) [526]
3.6.27
\(\int \genfrac {}{}{}{}{d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 g+2 h x}} \, dx\) [527]
3.6.28
\(\int \genfrac {}{}{}{}{d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx\) [528]
3.6.29
\(\int \genfrac {}{}{}{}{1}{2+e^{-x}+e^x} \, dx\) [529]
3.6.30
\(\int \genfrac {}{}{}{}{x}{2+e^{-x}+e^x} \, dx\) [530]
3.6.31
\(\int \genfrac {}{}{}{}{x^2}{2+e^{-x}+e^x} \, dx\) [531]
3.6.32
\(\int \genfrac {}{}{}{}{1}{2+f^{-c-d x}+f^{c+d x}} \, dx\) [532]
3.6.33
\(\int \genfrac {}{}{}{}{x}{2+f^{-c-d x}+f^{c+d x}} \, dx\) [533]
3.6.34
\(\int \genfrac {}{}{}{}{x^2}{2+f^{-c-d x}+f^{c+d x}} \, dx\) [534]
3.6.35
\(\int \genfrac {}{}{}{}{1}{2+3^{-x}+3^x} \, dx\) [535]
3.6.36
\(\int \genfrac {}{}{}{}{1}{1-e^{-x}+2 e^x} \, dx\) [536]
3.6.37
\(\int \genfrac {}{}{}{}{1}{a+b e^{-x}+c e^x} \, dx\) [537]
3.6.38
\(\int \genfrac {}{}{}{}{x}{a+b e^{-x}+c e^x} \, dx\) [538]
3.6.39
\(\int \genfrac {}{}{}{}{x^2}{a+b e^{-x}+c e^x} \, dx\) [539]
3.6.40
\(\int \genfrac {}{}{}{}{1}{a+b f^{-c-d x}+c f^{c+d x}} \, dx\) [540]
3.6.41
\(\int \genfrac {}{}{}{}{x}{a+b f^{-c-d x}+c f^{c+d x}} \, dx\) [541]
3.6.42
\(\int \genfrac {}{}{}{}{x^2}{a+b f^{-c-d x}+c f^{c+d x}} \, dx\) [542]
3.6.43
\(\int \genfrac {}{}{}{}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {f+g x}}})^n}{d f+(e f+d g) x+e g x^2} \, dx\) [543]
3.6.44
\(\int \genfrac {}{}{}{}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {f+g x}}})^3}{d f+(e f+d g) x+e g x^2} \, dx\) [544]
3.6.45
\(\int \genfrac {}{}{}{}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {f+g x}}})^2}{d f+(e f+d g) x+e g x^2} \, dx\) [545]
3.6.46
\(\int \genfrac {}{}{}{}{a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {f+g x}}}}{d f+(e f+d g) x+e g x^2} \, dx\) [546]
3.6.47
\(\int \genfrac {}{}{}{}{1}{d f+(e f+d g) x+e g x^2} \, dx\) [547]
3.6.48
\(\int \genfrac {}{}{}{}{1}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {f+g x}}}) (d f+(e f+d g) x+e g x^2)} \, dx\) [548]
3.6.49
\(\int \genfrac {}{}{}{}{1}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {f+g x}}})^2 (d f+(e f+d g) x+e g x^2)} \, dx\) [549]
3.6.50
\(\int \genfrac {}{}{}{}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {d f-e f x}}})^n}{d^2-e^2 x^2} \, dx\) [550]
3.6.51
\(\int \genfrac {}{}{}{}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {d f-e f x}}})^3}{d^2-e^2 x^2} \, dx\) [551]
3.6.52
\(\int \genfrac {}{}{}{}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {d f-e f x}}})^2}{d^2-e^2 x^2} \, dx\) [552]
3.6.53
\(\int \genfrac {}{}{}{}{a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {d f-e f x}}}}{d^2-e^2 x^2} \, dx\) [553]
3.6.54
\(\int \genfrac {}{}{}{}{1}{d^2-e^2 x^2} \, dx\) [554]
3.6.55
\(\int \genfrac {}{}{}{}{1}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {d f-e f x}}}) (d^2-e^2 x^2)} \, dx\) [555]
3.6.56
\(\int \genfrac {}{}{}{}{1}{(a+b F^{\genfrac {}{}{}{}{c \sqrt {d+e x}}{\sqrt {d f-e f x}}})^2 (d^2-e^2 x^2)} \, dx\) [556]
3.6.57
\(\int \genfrac {}{}{}{}{(F^{\genfrac {}{}{}{}{\sqrt {1-a x}}{\sqrt {1+a x}}})^n}{1-a^2 x^2} \, dx\) [557]
3.6.58
\(\int \genfrac {}{}{}{}{F^{\genfrac {}{}{}{}{3 \sqrt {1-a x}}{\sqrt {1+a x}}}}{1-a^2 x^2} \, dx\) [558]
3.6.59
\(\int \genfrac {}{}{}{}{F^{\genfrac {}{}{}{}{2 \sqrt {1-a x}}{\sqrt {1+a x}}}}{1-a^2 x^2} \, dx\) [559]
3.6.60
\(\int \genfrac {}{}{}{}{F^{\genfrac {}{}{}{}{\sqrt {1-a x}}{\sqrt {1+a x}}}}{1-a^2 x^2} \, dx\) [560]
3.6.61
\(\int \genfrac {}{}{}{}{F^{-\genfrac {}{}{}{}{\sqrt {1-a x}}{\sqrt {1+a x}}}}{1-a^2 x^2} \, dx\) [561]
3.6.62
\(\int \genfrac {}{}{}{}{F^{-\genfrac {}{}{}{}{2 \sqrt {1-a x}}{\sqrt {1+a x}}}}{1-a^2 x^2} \, dx\) [562]
3.6.63
\(\int a^x b^x x^2 \, dx\) [563]
3.6.64
\(\int a^x b^x x \, dx\) [564]
3.6.65
\(\int a^x b^x \, dx\) [565]
3.6.66
\(\int \genfrac {}{}{}{}{a^x b^x}{x} \, dx\) [566]
3.6.67
\(\int \genfrac {}{}{}{}{a^x b^x}{x^2} \, dx\) [567]
3.6.68
\(\int \genfrac {}{}{}{}{a^x b^x}{x^3} \, dx\) [568]
3.6.69
\(\int a^x b^x c^x \, dx\) [569]
3.6.70
\(\int a^x b^{-x} \, dx\) [570]
3.6.71
\(\int a^x b^{-x} x^2 \, dx\) [571]
3.6.72
\(\int \genfrac {}{}{}{}{(d+e e^{h+i x}) (f+g x)^3}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx\) [572]
3.6.73
\(\int \genfrac {}{}{}{}{(d+e e^{h+i x}) (f+g x)^2}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx\) [573]
3.6.74
\(\int \genfrac {}{}{}{}{(d+e e^{h+i x}) (f+g x)}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx\) [574]
3.6.75
\(\int \genfrac {}{}{}{}{d+e e^{h+i x}}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx\) [575]
3.6.76
\(\int \genfrac {}{}{}{}{d+e e^{h+i x}}{(a+b e^{h+i x}+c e^{2 h+2 i x}) (f+g x)} \, dx\) [576]
3.6.77
\(\int \genfrac {}{}{}{}{d+e e^{h+i x}}{(a+b e^{h+i x}+c e^{2 h+2 i x}) (f+g x)^2} \, dx\) [577]
3.6.78
\(\int \genfrac {}{}{}{}{(b e-a e e^{c+d x}) x}{b e-2 a e e^{c+d x}-b e e^{2 (c+d x)}} \, dx\) [578]
3.6.79
\(\int F^{a+b \log (c+d x^n)} x^2 \, dx\) [579]
3.6.80
\(\int F^{a+b \log (c+d x^n)} x \, dx\) [580]
3.6.81
\(\int F^{a+b \log (c+d x^n)} \, dx\) [581]
3.6.82
\(\int \genfrac {}{}{}{}{F^{a+b \log (c+d x^n)}}{x} \, dx\) [582]
3.6.83
\(\int \genfrac {}{}{}{}{F^{a+b \log (c+d x^n)}}{x^2} \, dx\) [583]
3.6.84
\(\int \genfrac {}{}{}{}{F^{a+b \log (c+d x^n)}}{x^3} \, dx\) [584]
3.6.85
\(\int F^{a+b \log (c+d x^n)} (d x)^m \, dx\) [585]
3.6.86
\(\int e^{\log ^2((d+e x)^n)} (d+e x)^m \, dx\) [586]
3.6.87
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} (d g+e g x)^m \, dx\) [587]
3.6.88
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} (d g+e g x)^2 \, dx\) [588]
3.6.89
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} (d g+e g x) \, dx\) [589]
3.6.90
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} \, dx\) [590]
3.6.91
\(\int \genfrac {}{}{}{}{F^{f (a+b \log ^2(c (d+e x)^n))}}{d g+e g x} \, dx\) [591]
3.6.92
\(\int \genfrac {}{}{}{}{F^{f (a+b \log ^2(c (d+e x)^n))}}{(d g+e g x)^2} \, dx\) [592]
3.6.93
\(\int \genfrac {}{}{}{}{F^{f (a+b \log ^2(c (d+e x)^n))}}{(d g+e g x)^3} \, dx\) [593]
3.6.94
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} (g+h x)^m \, dx\) [594]
3.6.95
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} (g+h x)^3 \, dx\) [595]
3.6.96
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} (g+h x)^2 \, dx\) [596]
3.6.97
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} (g+h x) \, dx\) [597]
3.6.98
\(\int F^{f (a+b \log ^2(c (d+e x)^n))} \, dx\) [598]
3.6.99
\(\int \genfrac {}{}{}{}{F^{f (a+b \log ^2(c (d+e x)^n))}}{g+h x} \, dx\) [599]
3.6.100
\(\int \genfrac {}{}{}{}{F^{f (a+b \log ^2(c (d+e x)^n))}}{(g+h x)^2} \, dx\) [600]
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