IFRS - Campus Rio Grande Matemática 2 Formulário de integrais indefinidas

1. Profª Débora Bastos

2. Mais fórmulas básicas
vn + 1 d(v n ) n − 1 dv
5 − ∫ v n dv =
n + 1
+ k
dx
= nv
dx
dv d(lnv) 1 dv
6 − ∫ v
= ln v + k
dx
=
v
⋅
dx
av d(a v )
7 − ∫ a v dv =
ln a
+ k
dx
v
= a . ln a ⋅
dv
dx
d(ev )
∫e
v v dv
8 − dv = e + k v
= e ⋅
dx dx

3. Exemplos: 5 − ∫ tgxdx 6 − ∫ cotgxdx
x
∫ ( 2x + 5) dx 7 − ∫ 1 − 4x2 dx 8 − ∫ 2x dx
2
1 −
2 − ∫  x 5x2 − 3 dx
 
  9 − ∫ 3tg4x sec24xdx
dx
∫e
x2
3 − ∫ 1 − 5x
10 − ∫e
3x
dx 11 − xdx
3 x2
x e x 1 + 2 ln x
4 − ∫ x4 + 2
dx 12 − ∫ 1 + ex
2
dx 13 −
∫ x
dx
Fórmulas decorrentes de combinações de
outras fórmulas:
15 − ∫ tgvdv = ln(sec v) + k
16 − ∫ cotgvdv = ln(senv) + k

4. Fórmulas relacionadas a funções
trigonométricas.
d(cosv) dv
9 − ∫ senvdv = - cos v + k dx
= −senv ⋅
dx
10 − ∫ cosvdv = senv + k d(senv)
= cos v ⋅
dv
dx dx
11 − ∫ sec2vdv = tgv + k d(tgv) 2
= sec v ⋅
dv
dx dx
12 − ∫ cosec2vdv = − cotgv + k d(cotgv)
= cosec2v ⋅ dv
dx dx
13 − ∫ cosec v.cotgv.dv = − cosec v + k
d(cosecv) dv
= −cosecv ⋅ cot gv ⋅
dx dx
14 − ∫ sec v.tgv.dv = sec v + k
d(secv) dv
= secv ⋅ tgv ⋅
dx dx

5. Exemplos:
sen( lnx)
1 − ∫ x dx
2 − ∫ cos23x ⋅ sen3x ⋅ dx
3 − ∫ (4secx ⋅ tgx − 5cosec2x)dx
4 − ∫ xcosx2dx
xsen 1 - x2
5 − ∫ 1 - x2
dx
(
tg e −3x ) dx
6 − ∫ e3x