basic integral rules

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Last updated 1:44 PM on 9/10/26
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20 Terms

1
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int kf(u)du

k x intf(u)du

2
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int(f(u)+g(u)du

intf(u)du + intg(u)du

3
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int du

u+c

4
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intu^ndu

1/(n+1)u^(n+1)+c

5
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int (1/u)du

ln|u|+c

6
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inte^udu

e^u+c

7
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inta^udu

(1/(ln(a))a^u+c

8
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int sin(u)du

-cos(u)+c

9
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int cos(u)du

sin(u)+c

10
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int tan(u)du

-ln|cos(u)|+c

11
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int cot(u)du

ln|sin(u)|+c

12
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int sec(u)du

ln|sec(u)+tan(u)|+c

13
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int csc(u)du

-ln|csc(u)+cot(u)|+c

14
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int sec²(u)du

tan(u)+c

15
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int csc²(u)du

-cot(u)+c

16
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int sec(u)tan(u)du

sec(u)+c

17
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int csc(u)cot(u)du

-csc(u)+c

18
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int 1/(sqroot(a²-u²)) du

arcsin(u/a)+c

19
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int 1/(a²-u²) du

1/a arctan(u/a)+c

20
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int 1/u(sqroot(u²-a²) du

1/a arcsec(|u|/a)+c