Ch 5 Identities Flashcards
∫du
u+C
∫kf(u)du
K∫f(u)du
∫du/u or ∫1/u(du)
Ln|u|+C
∫[f(u)+/-g(u)]du
∫f(u) +/- ∫g(u)
∫u^n du
(U^n+1)/n+1
∫e^udu
e^u + C
∫a^udu
(1/lna)a^u + C
∫sinudu
-cosu + C
∫cosudu
Sinu + C
∫tanudu
-ln |cosu| + C
∫cotudu
Ln|sinu| + C
∫secudu
ln |secu +tanu| + C
∫cscudu
-ln |cscu +cotu| + C
∫sec^2udu
Tanu + C
∫csc^2udu
-cotu + C
∫secutanudu
Secu + C
∫cscucotudu
-cscu + C
d/dx(cu)
cu`
d/dx(sinu)
(Cosu)u`
d/dx(cosu)
-(Sinu)u`
d/dx(tanu)
(Sec^2u)u`
d/dx(cotu)
-(Csc^2u)u`
d/dx(secu)
(Secutanu)u`
d/dx(cscu)
-(Cscucotu)u`
d/dx(u +/- v)
u +/- v
d/dx(uv)
uv+vu
d/dx(u/v)
uv - vu/ v^2
d/dx(c)
0
d/dx(u^n)
nu^n-1(u`)
d/dx(x)
1
d/dx(|u|)
(u/|u|)(u`)
d/dx(lnu)
u`/u
d/dx(e^u)
e^u(u`)
d/dx(loga u)
u`/(u)(lna)
d/dx(a^u)
(a^u)(lna)(u`)
d/dx(arcsinu)
u’/√1-u^2
d/dx(arccosu)
-u’/√1-u^2
d/dx(arctanu)
u`/1+u^2
d/dx(arccotu)
-u`/1+u^2
d/dx(arcsecu)
u’/|u|√[(u^2)-1]
d/dx(arccscu)
-u’/|u|√[(u^2)-1]
∫du/√[(a^2)-(u^2)] or ∫1/√[(a^2)-(u^2)] (du)
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
