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Formas básicas
Formas que incluyen
27. (^) L A 2 ax + bBn dx = (^2) a^ A^2 ax^ +^ bB 28. (^) L^2 axx^ +^ bdx = 22 ax + b + bLx 2 ax^ dx + b
n + 2 n + 2 +^ C,^ n^ Z -^2
Lxsax^ +^ bd-^2 dx^ =^ a^12 c^ ln^ ƒ^ ax^ +^ b^ ƒ^ +^ ax^ b+^ b^ d^ +^ C Lxsax^ dx^ +^ bd^ =^1 b^ ln^ ^ ax^ x+^ b^^ +^ C
Lsax^ +^ bd-^1 dx^ =^1 a^ ln^ ƒ^ ax^ +^ b^ ƒ^ +^ C Lxsax^ +^ bd-^1 dx^ =^ xa^ -^ ab^2 ln^ ƒ^ ax^ +^ b^ ƒ^ +^ C
Lxsax^ +^ bdn^ dx^ =^
sax + bdn^ +^1 a^2 caxn^ ++^2 b^ -^ n^ b+^1 d^ +^ C,^ n^ Z -1,^ -^2
Lsax^ +^ bdn^ dx^ =^
sax as (^) n+ +b d 1 n^ d+ 1 + C, n Z - 1
ax b
L 2 a^ dx^2 + x^2 =^ senh-^1 xa^ +^ C^ sa^7 0 d L 2 x^2 dx^ - a^2 =^ cosh-^1 xa^ +^ C^ sx^7 a^7 0 d
La^2 dx+^ x^2 =^1 a^ tan-^1 xa^ +^ C Lx 2 x^ dx^2 - a^2 =^1 a^ sec-^1 ^ ax^^ +^ C
L cosh^ x^ dx^ =^ senh^ x^ +^ C L 2 a^ dx^2 - x^2 =^ sen-^1 xa^ +^ C
L cot^ x^ dx^ =^ ln^ ƒ^ sen^ x^ ƒ^ +^ C L senh^ x^ dx^ =^ cosh^ x^ +^ C
L csc^ x^ cot^ x^ dx^ = -csc^ x^ +^ C L tan^ x^ dx^ =^ ln^ ƒ^ sec^ x^ ƒ^ +^ C
L csc^2 x^ dx^ = -cot^ x^ +^ C L sec^ x^ tan^ x^ dx^ =^ sec^ x^ +^ C
L cos^ x^ dx^ =^ sen^ x^ +^ C L sec^2 x^ dx^ =^ tan^ x^ +^ C
Lax^ dx^ =^ a L sen^ x^ dx^ = -cos^ x^ +^ C
x ln a +^ C^ sa^7 0,^ a^ Z^1 d
L^ dxx^ =^ ln^ ƒ^ x^ ƒ^ +^ C Lex^ dx^ =^ ex^ +^ C
L xn^ dx^ =^ x^
n + 1 Lk^ dx^ =^ kx^ +^ C^ scualquier número^ kd^ n^ +^1 +^ C^ sn^ Z -^1 d
T-
BREVE TABLA DE INTEGRALES
**29. (a) (b)
- 31.**
Formas que incluyen
Formas que incluyen
Formas que incluyen
53. (^) L 2 x^2 - a^2 dx = x 2 2 x^2 - a^2 - a 22 ln (^) ƒx + 2 x^2 - a^2 ƒ + C
L 2 x^2 dx^ - a^2 =^ ln^ ƒx^ +^2 x^2 -^ a^2 ƒ +^ C
x^2 a^2
Lx^2 2 a^ dx^2 - x^2 = -^2 a
(^2) - x 2 a^2 x +^ C
Lx 2 a^ dx^2 - x^2 = -^1 a^ ln^ ^ a^ +^2 a x 2 -^ x^2^ +^ C L^ x
2 2 a^2 - x^2 dx^ =^ a 22 sen-^1 xa^ -^12 x^2 a^2 -^ x^2 +^ C
L^2 a
(^2) - x 2 x^2 dx^ = -sen-^1 xa^ -^2 a
(^2) x (^) - x (^2) + C L^2 a
(^2) x - x (^2) dx = 2 a (^2) - x (^2) - a ln a + (^2) xa 2 - x (^2) + C
Lx^2 2 a^2 -^ x^2 dx^ =^ a 84 sen-^1 xa^ -^18 x^2 a^2 -^ x^2 sa^2 -^2 x^2 d^ +^ C^ L^
L 2 a^ dx^2 - x^2 =^ sen-^1 xa^ +^ C^2 a^2 -^ x^2 dx^ =^2 x^2 a^2 -^ x^2 +^ a^22 sen-^1 xa^ +^ C
La^2 dx-^ x^2 =^21 a^ ln^ ^ xx^ +-^ aa^^ +^ C L^ sa^2 dx-^ x^2 d^2 =^2 a^2 sa^2 x^ -^ x^2 d^ +^41 a^3 ln^ ^ xx^ +-^ aa^^ +^ C
a^2 x^2
Lx^2 2 a^ dx^2 + x^2 = -^2 a
(^2) + x 2 Lx 2 a^ dx^2 + x^2 = -^1 a^ ln^ `^ a^ +^2 a^ a^2 x^ +^ C
L x 2 + x (^2) ` + C 2 a^2 x^2 + x^2 dx^ = -^ a^22 ln^ Ax^ +^2 a^2 +^ x^2 B^ +^ x^2 a^22 +^ x^2 +^ C
L^2 a^2 x^2 +^ x^2 dx^ =^ ln^ Ax^ +^2 a^2 +^ x^2 B^ -^2 a^2 x^ +^ x^2 +^ C
L^2 a
L (^2) x (^) + x (^2) dx = 2 a (^2) + x (^2) - a ln a + (^2) xa 2 + x (^2) + C x^2 2 a^2 + x^2 dx = x 8 sa^2 + 2 x^2 d 2 a^2 + x^2 - a 84 ln (^) Ax + 2 a^2 + x^2 B + C
L 2 a^2 +^ x^2 dx^ =^ x^2 2 a^2 +^ x^2 +^ a^22 ln^ Ax^ +^2 a^2 +^ x^2 B^ +^ C
L 2 a^ dx^2 + x^2 =^ senh-^1 xa^ +^ C^ =^ ln^ Ax^ +^2 a^2 +^ x^2 B^ +^ C
La^2 dx+^ x^2 =^1 a^ tan-^1 ax^ +^ C L^ sa^2 dx+^ x^2 d^2 =^2 a^2 sa^2 x^ +^ x^2 d^ +^21 a^3 tan-^1 ax^ +^ C
a^2 x^2
L^2 axx^2 +^ bdx^ = -^2 axx^ +^ b+^ a^2 Lx 2 ax^ dx + b +^ C Lx^2 2 dxax + b = -^2 axbx^ +^ b-^2 abLx 2 ax^ dx + b +^ C
Lx 2 ax^ dx + b =^21 b ln^ ^22 axax^ ++^ bb^ - +^22 bb^ +^ C Lx 2 ax^ dx - b =^22 b tan-^1 A^ ax^ b-^ b+^ C
T-2 Breve tabla de integrales
Formas trigonométricas inversas
108. Lxn^ tan-^1 ax dx = (^) nx n+^ + 11 tan-^1 ax - (^) n +a (^1) L 1 x n+^ + 1 a^ dx (^2) x 2 , n Z - 1
Lxn^ cos-^1 ax^ dx^ =^ x n n+^ + 11 cos-^1 ax^ +^ n +a 1 L^ x
n + (^1) dx 21 - a^2 x^2 ,^ n^ Z -^1
Lxn^ sen-^1 ax^ dx^ =^ x n n+^ + 11 sen-^1 ax^ -^ n +a 1 L^ x
n + (^1) dx 21 - a^2 x^2 ,^ n^ Z -^1
L tan-^1 ax^ dx^ =^ x^ tan-^1 ax^ -^21 a^ ln^ s^1 +^ a^2 x^2 d^ +^ C
L sen-^1 ax^ dx^ =^ x^ sen-^1 ax^ +^1 a^21 -^ a^2 x^2 +^ C L cos-^1 ax^ dx^ =^ x^ cos-^1 ax^ -^1 a^21 -^ a^2 x^2 +^ C
L cscn^ ax^ cot^ ax^ dx^ = -^ csc nan^ ax +^ C,^ n^ Z^0 L secn^ ax^ tan^ ax^ dx^ =^ sec
L (^) nan (^) ax + C, n Z 0 cscn^ ax dx = - cscna^ - s^2 n^ ax-^ cot 1 d ax+ n n^ - -^21 L cscn^ -^2 ax dx, n Z 1
L secn^ ax^ dx^ =^ sec
n - (^2) ax tan ax asn - 1 d +^ n^ n^ - -^21 L secn^ -^2 ax^ dx,^ n^ Z^1
L sec^2 ax^ dx^ =^1 a^ tan^ ax^ +^ C L csc^2 ax^ dx^ = -^1 a^ cot^ ax^ +^ C
Lsec^ ax^ dx^ =^1 a^ ln^ ƒ^ sec^ ax^ +^ tan^ ax^ ƒ^ +^ C Lcsc^ ax^ dx^ = -^1 a^ ln^ ƒ^ csc^ ax^ +^ cot^ ax^ ƒ^ +^ C
L cotn^ ax^ dx^ = -^ cot
n - (^1) ax L tann^ ax^ dx^ =^ tan asn^ -^1 d^ -^ L cotn^ -^2 ax^ dx,^ n^ Z^1
n - (^1) ax asn - 1 d -^ L tann^ -^2 ax^ dx,^ n^ Z^1
L tan^2 ax^ dx^ =^1 a^ tan^ ax^ -^ x^ +^ C L cot^2 ax^ dx^ = -^1 a^ cot^ ax^ -^ x^ +^ C
Ltan^ ax^ dx^ =^1 a^ ln^ ƒ^ sec^ ax^ ƒ^ +^ C Lcot^ ax^ dx^ =^1 a^ ln^ ƒ^ sen^ ax^ ƒ^ +^ C
Lxn^ cos^ ax^ dx^ =^ x an sen^ ax^ -^ na Lxn^ sen^ ax^ dx^ = -^ x Lxn^ -^1 sen^ ax^ dx an cos^ ax^ +^ na Lxn^ -^1 cos^ ax^ dx
Lx^ sen^ ax^ dx^ =^ a^12 sen^ ax^ -^ xa^ cos^ ax^ +^ C Lx^ cos^ ax^ dx^ =^ a^12 cos^ ax^ +^ xa^ sen^ ax^ +^ C
L^1 +^ dxcos^ ax^ =^1 a^ tan^ ax^2 +^ C L^1 -^ dxcos^ ax^ = -^1 a^ cot^ ax^2 +^ C
Lb^ +^ c^ dx^ cos^ ax^ =^ a 2 c^21 - b^2 ln^ ^ c^ +^ b^ cos^ axb^ ++^ c^2 cosc^2 ax^ -^ b^2 sen^ ax^ +^ C,^ b^2 6 c^2
Lb^ +^ c^ dx^ cos^ ax^ =^ a 2 b^22 - c^2 tan-^1 cA^ bb^ - +^ cc^ tan^ ax^2 d^ +^ C,^ b^2 7 c^2
L^1 +^ dxsen^ ax^ = -^1 a^ tan^ ap^4 -^ ax^2 b^ +^ C L^1 -^ dxsen^ ax^ =^1 a^ tan^ ap^4 +^ ax^2 b^ +^ C
Lb^ +^ c^ dx^ sen^ ax^ =^ a 2 c-^2 1 - b^2 ln^ ^ c^ +^ b^ sen^ axb^ ++^ c^2 senc^2 ax^ -^ b^2 cos^ ax^ +^ C,^ b^2 6 c^2
Lb^ +^ c^ dx^ sen^ ax^ =^ a 2 b-^2 2 - c^2 tan-^1 cA^ bb^ - +^ cc^ tan^ ap^4 -^ ax^2 b d^ +^ C,^ b^2 7 c^2
T-4 Breve tabla de integrales
Formas exponenciales y logarítmicas
Formas que incluyen
Formas hiperbólicas
133. (^) L senhn^ ax dx = senhn^ -^1 naax^ cosh^ ax- n^ - n (^1) L senhn^ -^2 ax dx, n Z 0
L senh^2 ax^ dx^ =^ senh^4 a^2 ax -^2 x^ +^ C L cosh^2 ax^ dx^ =^ senh^4 a^2 ax +^ x^2 +^ C
Lsenh^ ax^ dx^ =^1 a^ cosh^ ax^ +^ C Lcosh^ ax^ dx^ =^1 a^ senh^ ax^ +^ C
L 22 xax^ dx - x^2 =^ a^ sen-^1 ax^ - a^ ab^ -^22 ax^ -^ x^2 +^ C Lx 22 ax^ dx - x^2 = -^1 a^ A^2 a^ x-^ x +^ C
L^22 ax^ -^ x
2 x^2 dx^ = -^2 A^2 a^ x-^ x-^ sen-^1 ax^ - a^ ab^ +^ C
L^22 ax^ -^ x
L x 2 dx = 22 ax - x (^2) + a sen- (^1) ax - a ab + C x 22 ax - x^2 dx = sx^ +^ ads^2 x^ -^63 ad^22 ax^ -^ x^2 + a 23 sen-^1 ax^ - a^ ab + C
L A 22 ax^ dx - x^2 Bn^ =^
sx - adA 22 ax - x^2 B^2 -^ n sn - 2 da^2 +^ snn - - 23 da^2 L A 22 ax^ dx - x^2 Bn^ -^2
L A^22 ax^ -^ x^2 B
n (^) dx = sx^ -^ adAn^2 +^2 ax 1 -^ x^2 Bn+ (^) n na+^2 L A^22 ax^ -^ x^2 B
n - (^2) dx
L 22 ax^ -^ x^2 dx^ =^ x^ -^2 a^22 ax^ -^ x^2 +^ a
2 2 sen-^1 ax^ - a^ ab^ +^ C
L 22 ax^ dx - x^2 =^ sen-^1 ax^ - a^ ab^ +^ C
2 2 ax x^2 , a > 0
Lx-^1 sln^ axdm^ dx^ =^ Lx^ ln^ dx^ ax^ =^ ln^ ƒ^ ln^ ax^ ƒ^ +^ C
L sln m ax +d m 1 + 1 + C, m Z - 1 xnsln axdm^ dx = xn^ +n^1 s ln+ ax 1 dm - (^) n m+ (^1) Lxnsln axdm^ -^1 dx, n Z - 1
Leax^ cos^ bx^ dx^ =^ e Lln^ ax^ dx^ =^ x^ ln^ ax^ -^ x^ +^ C
ax a^2 + b^2 sa^ cos^ bx^ +^ b^ sen^ bxd^ +^ C
Leax^ sen^ bx^ dx^ =^ e
ax a^2 + b^2 sa^ sen^ bx^ -^ b^ cos^ bxd^ +^ C
Lxnbax^ dx^ =^ x
nbax a ln b -^ a lnn b (^) Lxn^ -^1 bax^ dx,^ b^7 0,^ b^ Z^1
Lxeax^ dx^ =^ e Lxneax^ dx^ =^1 a^ xneax^ -^ naLxn^ -^1 eax^ dx
ax a^2 sax^ -^1 d^ +^ C
Lbax^ dx^ =^1 a^ b
ax Leax^ dx^ =^1 a^ eax^ +^ C^ ln^ b^ +^ C,^ b^7 0,^ b^ Z^1
Breve tabla de integrales T-
