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### Matematica2 8

• 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
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