Lucas Flashcards
Memorizartion
d/dx * (sinx) =
cos(x)
d/dx * (cosx) =
-sin(x)
d/dx * (tanx) =
sec^2 (x)
d/dx * (cscx) =
-cscxcotx
d/dx * (secx) =
secxtanx
d/dx * (cotx) =
- csc^2(x)
sin^2(x) + cos^2(x) =
1
1 - cos^2(x) =
sin^2(x)
1 - sin^2(x) =
cos^2(x)
tan^2(x) + 1 =
sec^2(x)
sec^2(x) - 1 =
tan^2(x)
cot^2(x) + 1 =
csc^2(x)
csc^2(x) - 1 =
cot^2(x)
∫sec(x)dx
ln| secx + tanx | + C
sin(2x) =
2sinxcosx
∫sin(x)dx =
- cosx + C
∫sec^2(x) =
tanx + C
∫1/(x^2 + 1)dx =
arctan(x)
∫dx/x =
ln |x| + C
∫b^x dx =
(b^x) / ln(b) + C
∫cos(x)dx =
sin(x) +C
∫csc^2 (x) =
-cot(x) + C
∫1/(1 - x^2)^(1/2) =
arcsin(x) +C
∫sec(x)tan(x)dx =
sec(x) + C
∫csc(x)dx =
ln|cscx - cotx| + C
tan(2x) =
2tan(x) / (1 - tan^2(x))
cos(2x) =
cos^2(x) - sin^2(x)
2cos^2(x) - 1
1 - sin^2(x)
∫arcsin(x)dx =
(x)arcsin(x) + (1 + x^2)^(1/2) + C
∫arccos(x)dx =
(x)arccos(x) - (1 - x^2)^(1/2) + C
∫arctan(x)dx =
(x)arctan(x) - (1 / 2) * ln( 1 + x^2) + C
∫arccsc(x)dx =
(x)arccsc(x) + ln(x + (x^2 - 1)^(1/2 ))+ C
∫arcsec(x)dx =
(x)arcsec(x) - ln(x + (x + (x^2 +1)^(1/2)) + C
∫arccot(x)dx =
(x)arccot(x) + (1 / 2) * ln(1 + x^2) +C
d/dx arcsin(x) =
1 / ((1-x^2)^(1/2))
d/dx arccos(x) =
- 1 / ((1- x^2)^(1/2))
d/dx arctan(x) =
1 / (1 + x^2)
d/dx arccot(x) =
-1 / (1+ x^2)
d/dx arcsec(x) =
1 / (|x| * (x^2 - 1)^(1/2))
d/dx arccsc(x) =
-1 / (|x| * (x^2 - 1)^(1/2))
