563489578934

A–5 Integral Tables 673
L x2 cos x dx = 2x cos x + (x 2 - 2) sin x
L eax dx = eax
a
Definite Integrals
L0
q
x m-1
1 + x n dx = p>n
sin (mp>n) , n 7 m 7 0
L x2 sin x dx = 2x sin x - (x 2 - 2) cos x
L x3 e ax dx = e ax a x2
a - 3x2
a 2
e ax
+ 6x
a 3
- 6 a 4 b
L eax sin x dx =
a 2 (a sin x - cos x)
L xeax dx = e ax a x a - 1 a 2 b
+ 1
e ax
L eax cos x dx =
a 2 (a cos x - sin x)
L x2 e ax dx = e ax a x2
a
- 2x
a 2 + 2 a 3 b + 1
q
x a-1 e -x dx =≠(a), a 7 0, where
L0
≠(a + 1) = a≠(a)
≠(1) = 1; ≠A 1 B 2 = 1p
≠(n) = (n - 1)! if n is a positive integer
L0
L
L0
L0
L0
L0
L0
q
q
-q
q
q
q
q
q
x 2n e -ax2 dx = 1 # 3 # 5 Á (2n - 1) p
2 n+1 a n B a
e -a2 x 2 +bx dx = 1p
a eb2 >(4a 2) , a 7 0
e -ax cosbx dx =
e -ax sin bx dx =
a
a 2 + b 2 , a 7 0
b
a 2 + b 2 , a 7 0
e -a2 x 2 cosbx dx = 1p >4a 2
e-b2 , a 7 0
2a
x a-1 cos bx dx = ≠(a)
b a cos 1 2
x a-1 sinbx dx = ≠(a)
b a sin 1 2
pa, 0 6 a 6 1, b 7 0
pa, 0 6 |a| 6 1, b 7 0