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Integrals
The following general rules can be applied to all integrations, where f() and g() are functions.
| ∫ ( n f(x) ) dx | = | n ∫ f(x) dx |
| ∫ ( f(x) + g(x) ) dx | = | ∫ f(x) dx + ∫ g(x) dx |
| ∫ ( f(x) g(x) ) dx | = | f(x) ∫g(x) dx - ∫(d/dx( f(x) ) ∫g(x) dx) dx |
Integrals of Common Functions
| Function F(x) = y |
Integral ∫ y dx |
| xn | 1/(n + 1) xn+1 |
| 1/x | Ln x |
| eax | 1/a eax |
| Ln x | x Ln x - x |
| Logax | x Loga (x / e) |
| sin ax | -1/a cos ax |
| cos ax | 1/a sin ax |
| tan ax | -1/a Ln (cos ax) |
| cosec x | Ln(cosec x - cot x) |
| sec x | Ln( sec x + tan x) |
| cot x | Ln sin x |
| arcsin(x/a) | x arcsin(x/a) + √( a2 - x2) |
| arccos(x/a) | x arccos(x/a) - √( a2 - x2) |
| arctan(x/a) | x arctan(x/a) - a Ln √( a2 + x2) |