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Integration Rules
| Question | Answer |
|---|---|
| integral of c f(x) dx | c times integral of f(x) dx |
| integral of f(x) + g(x) dx | integral of f(x) dx + integral of g(x) dx |
| integral of k dx | kx+ C |
| integral of x^n dx (wih n not equal to 1) | x^(n+1)/(n+1) +C |
| integral of (1/x) dx | ln|x| +C |
| integral of e^x dx | e^x +C |
| integral of b^x dx | b^x (ln(b)) +C |
| integral of sin(x) dx | -cox(x)+C |
| integral of cos(x) dx | sin(x) +C |
| integral of sec^2(x) dx | tan(x) +C |
| integral of sec(x)tan(x) dx | sec(x) +C |
| integral of csc^2(x) dx | -cot(x) +C |
| integral of csc(x)cot(x) dx | -csc(x) +C |
| integral of tan(x) dx | ln|sec(x)| +C |
| integral of cot(x) dx | ln|sin(x)| +C |
| integral of sec(x) dx | ln|sec(x)+tan(x)| +C |
| integral of csc(x) dx | ln|csc(x)-cot(x)| +C |
| integral of 1/(a^2-u^2)^(1/2) du | arcsin(u/a) +C |
| integral of 1/(u^2+a^2) du | (1/a) arctan(u/a) +C |
| integral of 1/ [ u(u^2-a^2)^(1/2) ] du | (1/a) arcsec(u/a) +C |
| IBP integral of u dv | uv - integral of v du |
| substitution integral of f(g(x)) g'(x) dx | integral of f(u) du with u=g(x) |
| sin^2(x) + cos^2(x) | 1 |
| réduction du carré sin^2(a) | (1-cos(2a))/2 |
| réduction du carré cos^2(a) | (1+cos(2a))/2 |
| sin(2a) | 2sin(a)cos(a) |
| sub trigo avec (a^2-x^2)^(1/2), x=? | x=a sin(theta) |
| sub trigo avec (a^2+x^2)^(1/2), x=? | x=a tan(theta) |
| sub trigo avec (x^2-a^2)^(1/2), x=? | x=a sec(theta) |
Created by:
AntoineHerlin
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