EXAM 1 Flashcards
S a dx
ax + C
S x^n dx
x^n+1 / n+1
S (1/x) dx
ln |x| + c
S e^x dx
s^x + c
S a^x dx
a^x / ln(a) + c
S ln(x) dx
xln(x) - x + c
S cos(x) dx
sin(x) + c
S sin(x) dx
-cos(x) + c
S sec^2(x) dx
tan(x) + c
(ln(x))’
1/x
(e^x)’
e^x
a^x =
e^(x*ln(a))
logb(x) =
ln(x) / ln(b)
(arcsinx)’
1 / sqrt(1-x^2)
(arccosx)’
-1 / sqrt(1-x^2)
(arctanx)’
1 / 1 + x^2
(arcsec)’
1 / |x| sqrt(x^2-1)
(arccsc)’
-1 / |x| sqrt(x^2-1)
(arccot)’
-1 / 1+x^2
Integration by parts formula
S u dv = uv-Svdu
Functions hardest to easiest
LIATE (log, inverse, algebraic, trig, exponential)
S csc^2 dx
-cot(x) + c
S sec(x)tan(x) dx
sec(x) + c
S csc(x)cot(x) dx
-csc(x) + x
S tan(x) dx
ln |sec(x)| + c
S cot(x) dx
ln |sin(x)| +c
S sec(x) dx
ln |sec(x)+tan(x)| + c
S csc(x) dx
ln |csc(x) - cot(x)| + c
S sin^2(x) dx
S 1-cos(2x) / 2 dx
S cos^2(x) dx
S 1+cos(2x) / 2
1 - sin^2 u =
cos^2(u)
1 + tan^2 u =
sec^2(u)
sec^2 u - 1 =
tan^2(u)
sqrt(a^2-x^2) , x =
asin(u)
sqrt(a^2 + x^2), x =
atan(u)
sqrt(x^2-a^2), x =
asec(u)
