MA226 – Spring 2023 – Exam 1 Formula Sheet
[() ± ()] = ′() ± ′()
() = ⋅ −1, ∈ ℕ
() = 0, ∈ ℝ
[() ⋅ ()] = ′() ⋅ () + () ⋅ ′()
[
()
()
] =
′() ⋅ () − () ⋅ ′()
[()]2

(()) = ′(()) ⋅ ′()
sin = cos
cos = − sin
= ⋅ ln()
log() =
1
⋅ ln()
sinh =
− −
2
cosh =
+ −
2
1
sin
= csc
1
cos
= sec
1
tan
= cot
sin
cos
= tan sin2 + cos2 = 1 cosh2 − sinh2 = 1
= (ln + 1)
tan = sec2
cot = − csc2
sec = sec tan
csc = − csc cot
sinh = cosh
cosh = sinh
sin =
− −
2
sinh =
− −
2
cos =
− −
2
cosh =
+ −
2
= cos + sin
∫ ()
= () − ()
() = ()
∫ ()

= ∫ ()

+ ∫ ()

∫ ()
= − ∫ ()

∫ ()
= 0
∫ ()
→ = () → ∫
()
′()

()
()
∫ ()[()] = ()() − ∫ () [()]
= ∑
!
∞
=0
sin = ∑(−1) ⋅
2+1
(2 + 1)!
∞
=0
cos = ∑(−1)
∞
=0
⋅
2
(2)!
ln( + 1) = ∑(−1)+1 ⋅
!
∞
=1
sinh = ∑
2+1
(2 + 1)!
∞
=0
cosh = ∑
2
(2)!
∞
=0
() = ∫
sin
0
() = − ∫
cos
∞
() = ∫
−∞
() = ∫

ln

0

() =
2
√
⋅ ∫ −
2

0
() =
2
√
⋅ ∫
2
0
Γ() = ∫ −1 ⋅ −
∞
0
() = ∑
1
∞
=1
[First Order Linear Inhomogeneous] () = ∫ ()
[Bernoulli Substitution] = 1−