Antiderivatives - Canisius College Blogs

Antiderivatives
Suppose F and G are antiderivatives of f and g, respectively, so
that F
f and G
g.
Function
Antiderivative
Reason
cf x
cF x
d
dx
cF x
d
dx
F x
f x
g x
F x
G x
xn 1
n 1
d
dx
1
x
ln x
d
dx
ln x
ex
ex
d
dx
ex
ax
ax
ln a
d
dx
x n (n
1)
MAT 111: Calculus I
cf x
G x
xn 1
n 1
ax
ln a
x n (n
f x
1)
1
x
ex
ax
Chapter 4: Applications of Differentiation
g x
More Antiderivatives
Function
Antiderivative
Reason
cos x
sin x
d
dx
sin x
sec2 x
csc x cot x
sec x tan x
csc2 x
1
1
x2
1
1 x2
1
1 x2
cos x
d
dx
d
dx
tan x
csc x
d
dx
d
dx
sec x
cot x
d
dx
sin
1
x
d
dx
cos
1x
tan
1x
MAT 111: Calculus I
sin x
cos x
cos x
sin x
sec2 x
tan x
csc x
sec x
csc x cot x
sec x tan x
cot x
csc2 x
sin
1
1
d
dx
cos
1x
d
dx
tan
1x
x
1 x2
1
1 x2
1
1 x2
Chapter 4: Applications of Differentiation