Integrals and trig

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31 Terms

1
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int of cos(x)

sin(x) + c

2
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int sin(x)

-cos(x)

3
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int sec(x)²

tan(x) + c

4
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int sec(x)tan(x)

sec(x)

5
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int csc(x)cot(x)

-csc(x) + c

6
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int csc(x)²

-cot(x) + c

7
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int 1 / (a² + x²)

1/a arctan(x/a) + c

8
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int 1 / sqrt(a² - x²)

arcsin(x/a) + c

9
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int 1 / x(sqrt(x² - a²))

1/a arcsec(x/a) + c

10
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int enx

1/n enx + c

11
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derv enx

nenx

12
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int tan(x)

1/a ln(sec(ax)) or -1/a ln(cos(ax))

13
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int sec(x)

ln(sec(x) + tan(x))

14
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int cot(x)

ln(sin(x))

15
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int cot(x)2

-cot(x) -x

16
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int ax

ax / ln(a)

17
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int ax ln(a)

ax

18
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19
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int 2sec(x)2 tan(x)

sec(x)2

20
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sin(x)2 + cos(x)2 =

1

21
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1 + tan(x)2 =

sec(x)2

22
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1 + cot(x)2 =

csc(x)2

23
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sin(2x) =

2sin(x)cos(x)

24
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cos (2x) =

  • cos(x)2 - sin(x)2

  • 2cos(x)2 - 1

  • 1 - 2sin(x)2

25
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sin(x)2 =

(1 - cos(2x)) / 2

26
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cos(x)2

(1 + cos(2x)) / 2

27
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tan(x)2

(1 - cos(2x)) / (1 + cos(2x))

28
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Area of a semicircle

½ pi r2

29
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area of an Isoceles right triangle

½ b2

30
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Area of an equilateral triangle

sqrt(3) / 4 b2

31
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Pappues Theorem

V = A(2pi) R