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AP Cal
integration / differentiation | |
---|---|
∫Kf(u)du | k∫f(u)du |
∫[f(u)±g(u)]du | u+c |
∫a^u du | (1/ lna) a^u +c |
∫e^u du | e^u +c |
∫sinu du | -cosu +c |
∫cosu du | sinu +c |
∫tan u du | -ln |cosu| +c |
∫cotu du | ln |sinu| +c |
∫secu du | ln |secu + tanu| +c |
∫cscu du | -ln |cscu + cotu| +c |
∫sec^2u du | tanu +c |
∫csc^2u du | -cotu +c |
∫secutanu du | secu +c |
∫cscucotu du | -cscu +c |
∫du/√(a^2-u^2) | arcsin u/a +c |
∫du/ a^2 + u^2 | 1/a arctan u/a +c |
∫du/ |u| √u^2-a^2 | 1/a arcsec |u|/a +c |
d/dx [cu] | cu^1 |
d/dx [u±v] | u^1 ± v^1 |
d/dx [uv] | uv^1 + vu^1 |
d/dx [u/v] | vu^1-uv^1/ v^2 |
d/dx [c] | 0 |
d/dx [u^n] | nu^(n-1) u^1 |
d/dx [x] | 1 |
d/dx [|u|] | u/|u| (u^1) ; u≠0 |
d/dx [lnu] | u^1/ u |
d/dx [e^u] | e^u u^1 |
d/dx [log(a)u] | u^1 / (lna)u |
d/dx [a^u] | (lna) a^u u^1 |
d/dx [sinu] | (cosu) u^1 |
d/dx [cosu] | -(sinu) u^1 |
d/dx [tanu] | (sec^2 u) u^1 |
d/dx [cotu] | -(csc^1) u^1 |
d/dx [secu] | (secutanu) u^1 |
d/dx [cscu] | -(cscucotu) u^1 |
d/dx [arcsinu] | u^1 / √(1-u^2) |
d/dx [arccosu] | -u^1 / √(1-u^2) |
d/dx [arctanu] | u^1 / 1+u^2 |
d/dx [arccotu] | -u^1 / 1+u^2 |
d/dx [arcsecu] | u^1 / |u|√(u^2-1) |
d/dx [arccscu] | -u^1 / |u|√(u^2-1) |