Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: zz-x2580
MAST10006 Calculus 2 Formulae Sheet∫
sinx dx = − cosx+ C
∫
cosx dx = sinx+ C∫
secx dx = log | secx+ tanx|+ C
∫
cosecx dx = log |cosecx− cotx|+ C∫
sec2 x dx = tanx+ C
∫
cosec 2x dx = − cotx+ C∫
sinhx dx = coshx+ C
∫
coshx dx = sinhx+ C∫
sech 2x dx = tanhx+ C
∫
cosech 2x dx = − cothx+ C∫
1√
a2 − x2 dx = arcsin
(x
a
)
+ C
∫
1√
x2 + a2
dx = arcsinh
(x
a
)
+ C∫ −1√
a2 − x2 dx = arccos
(x
a
)
+ C
∫
1√
x2 − a2 dx = arccosh
(x
a
)
+ C∫
1
a2 + x2
dx =
1
a
arctan
(x
a
)
+ C
∫
1
a2 − x2 dx =
1
a
arctanh
(x
a
)
+ C
where a > 0 is constant and C is an arbitrary constant of integration.
cos2 x+ sin2 x = 1 cosh2 x− sinh2 x = 1
1 + tan2 x = sec2 x 1− tanh2 x = sech 2x
cot2 x+ 1 = cosec 2x coth2 x− 1 = cosech 2x
cos(2x) = cos2 x− sin2 x cosh(2x) = cosh2 x+ sinh2 x
cos(2x) = 2 cos2 x− 1 cosh(2x) = 2 cosh2 x− 1
cos(2x) = 1− 2 sin2 x cosh(2x) = 1 + 2 sinh2 x
sin(2x) = 2 sinx cosx sinh(2x) = 2 sinhx coshx
cos(x+ y) = cos x cos y − sinx sin y cosh(x+ y) = cosh x cosh y + sinhx sinh y
sin(x+ y) = sinx cos y + cosx sin y sinh(x+ y) = sinhx cosh y + coshx sinh y
coshx =
1
2
(
ex + e−x
)
sinhx =
1
2
(
ex − e−x)
cosx =
1
2
(
eix + e−ix
)
sinx =
1
2i
(
eix − e−ix)
eix = cosx+ i sinx arctanhx =
1
2
log
(
1 + x
1− x
)
arcsinhx = log(x+
√
x2 + 1) arccoshx = log(x+
√
x2 − 1)
lim
n→∞
1
np
= 0 (p > 0) lim
n→∞
rn = 0 (|r| < 1)
lim
n→∞
a
1
n = 1 (a > 0) lim
n→∞
n
1
n = 1
lim
n→∞
an
n!
= 0 (a ∈ R) lim
n→∞
log n
np
= 0 (p > 0)
lim
n→∞
(
1 +
a
n
)n
= ea (a ∈ R) lim
n→∞
np
an
= 0 (p ∈ R, a > 1)
