Standard Integrals
Trignometrical Formulae
sin(A + B) = sin A cos B + cos A sin B
sin(A − B) = sin A cos B − cos A sin B
Z
f (x)
f (x) dx
cos(A + B) = cos A cos B − sin A sin B
cos(A − B) = cos A cos B + sin A sin B
2
2
sin A + cos A = 1,
sin 2A = 2 sin A cos A
(ax + b)n
(ax + b)n+1
a (n + 1)
n 6= −1
cos 2A = 2 cos2 A − 1 = 1 − 2 sin2 A
sin x
− cos x
cos x
sin x
ex
ex
1
ax + b
1
ln(ax + b)
a
sinh x
cosh x
cosh x
sinh x
2 sin A cos B = sin(A + B) + sin(A − B)
2 cos A sin B = sin(A + B) − sin(A − B)
2 cos A cos B = cos(A + B) + cos(A − B)
2 sin A sin B = cos(A − B) − cos(A + B)
Hyperbolic Functions
sinh x =
ex − e−x
,
2
cosh x =
ex + e−x
2
Standard Derivatives
f (x)
f 0 (x)
xn
nxn−1
sin ax
uv
a cos ax
cos ax
−a sin ax
tan ax
a sec2 ax
eax
aeax
ln x
1
x
a sinh ax
uv
u0 v + u v 0
u
v
u0 v − u v 0
v2
u0 v dx
1
x
tan−1
a
a
1
a2 − x 2
1
a+x
ln
2a
a−x
1
x2 − a2
1
x−a
ln
2a
x+a
a cosh ax
cosh ax
uv −
Z
1
x2 + a2
√
sinh ax
0
1
a2 − x2
sin−1
x
a
√
√
1
x2 + a2
ln x +
1
x2 − a2
ln x +
√
√
x2 + a2
x 2 − a2