Level 575 Level 577
Level 576

Antiderivatives


91 words 0 ignored

Ready to learn       Ready to review

Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

All None

Ignore?
∫(c*f(x))dx
c*∫(f(x))dx
∫(f(x) +/- g(x))
∫(f(x)) +/- ∫(g(x))
x^(n+1)/(n+1)
∫(x^n)dx where n<>-1
∫(e^x)dx
e^x+C
∫(a^x)dx
a^x/lna+C
∫(x^-1)dx
ln(abs(x))
∫sin(x) dx
-cos(x)
∫cos(x) dx
sin(x)
∫sec^2(x)dx
tanx
∫(secxtanx)dx
secx
∫csc^2(x)dx
-cotx
∫(cscxcotx)dx
-cscx
∫sinhxdx
coshx
∫coshxdx
sinhx
∫sech²xdx
tanhx
∫(sechxtanhx)dx
-sechx
∫(1/√(1-x^2))dx
arcsinx
∫(1/(1+x^2))dx
arctanx
∫(sin kx)dx
-1/k cos kx
∫(cos kx)dx
1/k sin kx
∫(sec^2 kx)dx
1/k tan kx
∫(csc^2 kx)dx
-1/k cot kx
1/k sec kx
∫(sec kx tan kx)dx
-1/k csc kx
∫(csc kx cot kx)dx
∫(e^ kx)dx
1/k e^ kx
∫(1/x)dx
ln|x|+C
∫(1/√(1-k^2x^2))dx
1/k arcsin kx
∫(1/(1+k^2x^2))dx
1/k arctan kx
∫(1/(x*√(k^2x^2-1)))dx
arcsec kx, kx>1
∫(a^ kx)dx
(1/(k*ln a))*a^ kx, a>0 && a<>1
(logaX)'
1/(xlna)
(lnx)'
1/x
(a^x)'
(a^x)lna
(sinx)'
cosx
(cosx)'
-sinx
(tanx)'
sec²x
(cscx)'
-cscxcotx
(secx)'
secxtanx
(cotx)'
-csc²x
f(x+h)- f(x)/ h
Definition form of f(x)'
(au^(n+1))/(n+1)+C
∫ au^n ∗ du
-cosu+C
∫ sinu∗du
sinu+C
∫ cosu∗du
ln|secu|+C
∫ tanu∗du
ln|sinu|+C
∫ cotu∗du
ln|secu+tanu|+C
∫ secu∗du
ln|cscu-cotu|+C
∫ cscu∗du
tanu+C
∫ sec²u∗du
-cotu+C
∫csc^2u du
secu+C
∫ tanu∗secu∗du
-cscu+C
∫cotu cscu du
e^u + c
∫ e^u du
ln|u|+C
∫ 1/u∗du
sin⁻¹u+C
∫1/√1-u²∗du
tan⁻¹u+C
∫ 1/1+u²∗du
-1/(a-x^2)^.5
y' of arccosU
x^x(lnx+1)
d/dx (x^x)
∫sin u du
-cos u + C
∫cos u du
sin u + C
∫tan u du
-ln |cos u| + C
∫cot u du
ln |sin u| + C
∫sec u du
ln |sec u + tan u| + C
∫ csc u du
-ln |csc u + cot u| + C
∫ sec^2 u du
tan u + C
∫csc^2 u du
-cot u + C
sec u + C
∫sec u tan u du
-csc u + C
∫csc u cot u du
∫du/√(a^2 - u^2)
arcsin (u/a) + C
∫du/u√(u^2 - a^2)
(1/a) arcsec (|u|/a) + C
∫du/(a^2 + u^2)
(1/a) arctan (u/a) + C
∫ (u'/u)
ln |u| + C
∫ e^u
e^u + C
∫ a^u
(1/ln a) (a^u) + C
kx + c
∫ k dx
∫ x^n dx
(x^n+1/ n+1) + c
-cosx + c
∫ sinx dx
sinx + c
∫ cosx dx
tanx + c
∫ sec^2x dx
e^x + c
∫ e^x dx
∫ 1/x dx
ln lxl + c
∫ a^x dx
(a^x/ lna) + c
definite integral
has limits a & b, find antiderivative, F(b) - F(a)
indefinite integral
no limits, find antiderivative + C, use inital value to find C
FTC
The integral from a to b is equal to the antiderivative at a minus the antiderivative at b.
c
The unknown value that must be added to the antiderivative.
Arctanx + c
∫ 1/(1+x^2) dx
secx + C
∫ secx tanx dx
Csc+ C
∫ -cotx cscx dx
Cot x+ C
∫ -csc^2 x dx
ArcSin+ C
∫ 1/ ( 1-x^2 )^(1/2) dx
ArcCosx+C
∫ 1/ ( 1+x^2 )^(1/2) dx