integral rules

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20 Terms

1
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Integral of sin(x)

-cos(x) + C.

2
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Integral of cos(x)

sin(x) + C.

3
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Integral of sec^2(x)

tan(x) + C.

4
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Integral of csc^2(x)

-cot(x) + C.

5
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Integral of sec(x)tan(x)

sec(x) + C.

6
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Integral of csc(x)cot(x)

-csc(x) + C.

7
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Integral of e^(ax)

(1/a)e^(ax) + C.

8
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Integral of a^x

(1/ln(a))a^x + C.

9
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Integral of 1/x

ln|x| + C.

10
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Integral of x^n (n ≠ -1)

(x^(n+1))/(n+1) + C.

11
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Integral of sin^2(x)

(1/2)(x - sin(x)cos(x)) + C.

12
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Integral of cos^2(x)

(1/2)(x + sin(x)cos(x)) + C.

13
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Integral of tan(x)

-ln|cos(x)| + C.

14
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Integral of cot(x)

ln|sin(x)| + C.

15
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Integral of sec^3(x)

(1/2)(sec(x)tan(x) + ln|sec(x) + tan(x)|) + C.

16
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Integral of csc^3(x)

-(1/2)(csc(x)cot(x) + ln|csc(x) + cot(x)|) + C.

17
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Integral of arcsin(x)

x*arcsin(x) + sqrt(1-x^2) + C.

18
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Integral of arccos(x)

x*arccos(x) - sqrt(1-x^2) + C.

19
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Integral of arctan(x)

x*arctan(x) - (1/2)ln(1+x^2) + C.

20
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Integral of arcsec(x)

x*arcsec(x) - ln|x + sqrt(x^2-1)| + C.