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3.6
Integrals 501 to 600
3.6.1
\(\int \frac {1}{(x+\sqrt {-3-2 x+x^2})^2} \, dx\)
3.6.2
\(\int \frac {1}{(x+\sqrt {-3-2 x+x^2})^3} \, dx\)
3.6.3
\(\int \frac {1}{x+\sqrt {-3-4 x-x^2}} \, dx\)
3.6.4
\(\int \frac {1}{(x+\sqrt {-3-4 x-x^2})^2} \, dx\)
3.6.5
\(\int \frac {1}{(x+\sqrt {-3-4 x-x^2})^3} \, dx\)
3.6.6
\(\int x^3 (1+x)^3 (1+2 x) \sqrt {1-x^2-2 x^3-x^4} \, dx\)
3.6.7
\(\int (1+2 x) (x+x^2)^3 \sqrt {1-(x+x^2)^2} \, dx\)
3.6.8
\(\int \frac {(2 \sqrt {3-x}+\frac {3}{\sqrt {1+x}})^2}{x} \, dx\)
3.6.9
\(\int \frac {-1+x+x^2}{1+\sqrt {1+x^2}} \, dx\)
3.6.10
\(\int \frac {-1+x+x^2}{1+x+\sqrt {1+x^2}} \, dx\)
3.6.11
\(\int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx\)
3.6.12
\(\int (a+c \sqrt {x}+b x^{2/3})^2 \, dx\)
3.6.13
\(\int (a+c \sqrt {x}+b x^{2/3})^3 \, dx\)
3.6.14
\(\int \frac {-1+x^2}{\sqrt {a-b+\frac {b}{x^2}} x^3} \, dx\)
3.6.15
\(\int \frac {-1+x^2}{\sqrt {a+b (-1+\frac {1}{x^2})} x^3} \, dx\)
3.6.16
\(\int \frac {1+x}{(4+x^2) \sqrt {9+x^2}} \, dx\)
3.6.17
\(\int x (1+\sqrt {1-x^2}) \, dx\)
3.6.18
\(\int x (1+\sqrt {1-x} \sqrt {1+x}) \, dx\)
3.6.19
\(\int x (1+\frac {1}{\sqrt {2+x} \sqrt {3+x}}) \, dx\)
3.6.20
\(\int \frac {x-\sqrt {x^6}}{x (1-x^4)} \, dx\)
3.6.21
\(\int \frac {1-\frac {\sqrt {x^6}}{x}}{1-x^4} \, dx\)
3.6.22
\(\int \frac {x-\sqrt {x^6}}{x-x^5} \, dx\)
3.6.23
\(\int \frac {x}{x+\sqrt {x^6}} \, dx\)
3.6.24
\(\int \frac {\sqrt {x}-\sqrt {x^3}}{x-x^3} \, dx\)
3.6.25
\(\int \frac {1}{\sqrt {x}+\sqrt {x^3}} \, dx\)
3.6.26
\(\int \frac {1}{\sqrt {-1+x}+\sqrt {(-1+x)^3}} \, dx\)
3.6.27
\(\int (-\frac {3}{(4+5 x)^2}-\frac {5+4 x}{(4+5 x)^2 \sqrt {1-x^2}}) \, dx\)
3.6.28
\(\int \frac {-5-4 x-3 \sqrt {1-x^2}}{(4+5 x)^2 \sqrt {1-x^2}} \, dx\)
3.6.29
\(\int \frac {1}{(-5-4 x) \sqrt {1-x^2}+3 (1-x^2)} \, dx\)
3.6.30
\(\int \frac {1}{3-3 x^2-5 \sqrt {1-x^2}-4 x \sqrt {1-x^2}} \, dx\)
3.6.31
\(\int \frac {-1+\sqrt {1-x^2}}{\sqrt {1-x^2} (2+x-2 \sqrt {1-x^2})^2} \, dx\)
3.6.32
\(\int \frac {a+b x^{-1+n}}{c x+d x^n} \, dx\)
3.6.33
\(\int \frac {\sqrt {1+2 x^2}}{1+\sqrt {1+2 x^2}} \, dx\)
3.6.34
\(\int \frac {\sqrt {-1+4 x^2}}{x+\sqrt {-1+4 x^2}} \, dx\)
3.6.35
\(\int \frac {a+b x+c x^2}{(d+e x)^3 \sqrt {-1+x^2}} \, dx\)
3.6.36
\(\int \frac {1+2 x^8}{x (1+x^8)^{3/2}} \, dx\)
3.6.37
\(\int \frac {\sqrt {1+x^8} (1+2 x^8)}{x+2 x^9+x^{17}} \, dx\)
3.6.38
\(\int (1-9 x^2+\frac {x}{\sqrt {1-9 x^2}}) \, dx\)
3.6.39
\(\int \frac {x+(1-9 x^2)^{3/2}}{\sqrt {1-9 x^2}} \, dx\)
3.6.40
\(\int \frac {(-3+2 \sqrt {x}) (-3 \sqrt {x}+x)^{2/3}}{\sqrt {x}} \, dx\)
3.6.41
\(\int \frac {9-9 \sqrt {x}+2 x}{\sqrt [3]{-3 \sqrt {x}+x}} \, dx\)
3.6.42
\(\int \frac {1}{\sqrt {4-9 x^2}} \, dx\)
3.6.43
\(\int \frac {1}{\sqrt {2-3 x} \sqrt {2+3 x}} \, dx\)
3.6.44
\(\int \frac {1}{\sqrt {(2-3 x) (2+3 x)}} \, dx\)
3.6.45
\(\int \frac {1}{\sqrt {15-2 x-x^2}} \, dx\)
3.6.46
\(\int \frac {1}{\sqrt {3-x} \sqrt {5+x}} \, dx\)
3.6.47
\(\int \frac {1}{\sqrt {(3-x) (5+x)}} \, dx\)
3.6.48
\(\int \frac {1}{\sqrt {-15-8 x-x^2}} \, dx\)
3.6.49
\(\int \frac {1}{\sqrt {-3-x} \sqrt {5+x}} \, dx\)
3.6.50
\(\int \frac {1}{\sqrt {(-3-x) (5+x)}} \, dx\)
3.6.51
\(\int (1-\sqrt {x}) \, dx\)
3.6.52
\(\int \frac {1-x}{1+\sqrt {x}} \, dx\)
3.6.53
\(\int \sqrt {\frac {1}{1-x^2}} \, dx\)
3.6.54
\(\int \sqrt {\frac {1+x^2}{1-x^4}} \, dx\)
3.6.55
\(\int \sqrt {\frac {1}{-1+x^2}} \, dx\)
3.6.56
\(\int \sqrt {\frac {1+x^2}{-1+x^4}} \, dx\)
3.6.57
\(\int \frac {1}{\sqrt {1-x}} \, dx\)
3.6.58
\(\int \frac {\sqrt {1+x}}{\sqrt {1-x^2}} \, dx\)
3.6.59
\(\int \frac {1}{\sqrt {1+x}} \, dx\)
3.6.60
\(\int \frac {\sqrt {1-x}}{\sqrt {1-x^2}} \, dx\)
3.6.61
\(\int \sqrt {1-x} \, dx\)
3.6.62
\(\int \frac {\sqrt {1-x^2}}{\sqrt {1+x}} \, dx\)
3.6.63
\(\int \sqrt {1+x} \, dx\)
3.6.64
\(\int \frac {\sqrt {1-x^2}}{\sqrt {1-x}} \, dx\)
3.6.65
\(\int \frac {\sqrt {2+3 x}}{\sqrt {1+x}} \, dx\)
3.6.66
\(\int \frac {\sqrt {1-x} \sqrt {2+3 x}}{\sqrt {1-x^2}} \, dx\)
3.6.67
\(\int \frac {(1+x)^{3/2}}{(1-x)^{3/2} x} \, dx\)
3.6.68
\(\int \frac {(1+x)^3}{x (1-x^2)^{3/2}} \, dx\)
3.6.69
\(\int \frac {(1+a x)^{3/2}}{x (1-a x)^{3/2}} \, dx\)
3.6.70
\(\int \frac {(1+a x)^3}{x (1-a^2 x^2)^{3/2}} \, dx\)
3.6.71
\(\int \frac {1}{\sqrt {1-x^2}} \, dx\)
3.6.72
\(\int \frac {\sqrt {1+x^2}}{\sqrt {1-x^4}} \, dx\)
3.6.73
\(\int \frac {1}{\sqrt {1+x^2}} \, dx\)
3.6.74
\(\int \frac {\sqrt {1-x^2}}{\sqrt {1-x^4}} \, dx\)
3.6.75
\(\int \sqrt {1-x^2} \, dx\)
3.6.76
\(\int \frac {\sqrt {1-x^4}}{\sqrt {1+x^2}} \, dx\)
3.6.77
\(\int \sqrt {1+x^2} \, dx\)
3.6.78
\(\int \frac {\sqrt {1-x^4}}{\sqrt {1-x^2}} \, dx\)
3.6.79
\(\int \frac {1}{x-\sqrt {1+x^2}} \, dx\)
3.6.80
\(\int \frac {1}{x-\sqrt {1-x^2}} \, dx\)
3.6.81
\(\int \frac {1}{x-\sqrt {1+2 x^2}} \, dx\)
3.6.82
\(\int \frac {2 x-x^3+x^2 \sqrt {2-x^2}}{-2+2 x^2} \, dx\)
3.6.83
\(\int \frac {x \sqrt {2-x^2}}{x-\sqrt {2-x^2}} \, dx\)
3.6.84
\(\int \frac {x}{-x+\sqrt {2 x-x^2}} \, dx\)
3.6.85
\(\int \frac {x+\sqrt {2 x-x^2}}{2-2 x} \, dx\)
3.6.86
\(\int \frac {\sqrt {2-x} \sqrt {x}+x}{2-2 x} \, dx\)
3.6.87
\(\int \frac {\sqrt {x}}{\sqrt {2-x}-\sqrt {x}} \, dx\)
3.6.88
\(\int \frac {1}{((1+x) (-1+x^2))^{2/3}} \, dx\)
3.6.89
\(\int \frac {-1+x^2}{(1+x^2) \sqrt {x (1+x^2)}} \, dx\)
3.6.90
\(\int \frac {-1+x^2}{(1+x^2) \sqrt {x+x^3}} \, dx\)
3.6.91
\(\int \frac {\sqrt {\frac {(-1+x^2)^2}{x (1+x^2)}}}{1+x^2} \, dx\)
3.6.92
\(\int \frac {\sqrt {\frac {(-1+x^2)^2}{x+x^3}}}{1+x^2} \, dx\)
3.6.93
\(\int \frac {1}{\sqrt {a+\frac {b}{x^2}} \sqrt {c+d x^2}} \, dx\)
3.6.94
\(\int \frac {\sqrt {-2 x^2+x^4}}{(-1+x^2) (2+x^2)} \, dx\)
3.6.95
\(\int \frac {\sqrt {1-\frac {1}{(-1+x^2)^2}}}{2-x^2} \, dx\)
3.6.96
\(\int \frac {\sqrt {\frac {-2 x^2+x^4}{(-1+x^2)^2}}}{2+x^2} \, dx\)
3.6.97
\(\int (1+\frac {2 x}{1+x^2})^{5/2} \, dx\)
3.6.98
\(\int (1+\frac {2 x}{1+x^2})^{3/2} \, dx\)
3.6.99
\(\int \sqrt {1+\frac {2 x}{1+x^2}} \, dx\)
3.6.100
\(\int \frac {1}{\sqrt {1+\frac {2 x}{1+x^2}}} \, dx\)
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