Mathematical preliminaries - Continuous and Discrete Time Signals and Systems - page 796

= 1

a 3 (2 at cos at − 2 sin at + a 2 t 2 sin at ) + C , a = 0

t 2 cos at d t

1
a 3 (2 at sin at − 2 cos at − a 2 t 2 cos at ) + C , a = 0

t 2 sin at d t =

sin( a − b ) t
2( a − b )

sin( a + b ) t
2( a + b )

+ C , a 2 = b 2 cos at cos bt d t = +

sin( a − b ) t
2( a − b )

sin( a + b ) t
2( a + b )

+ C , a 2 = b 2

sin at sin bt d t = −

cos( a − b ) t
2( a − b )

cos( a + b ) t
2( a + b )

sin at cos bt d t =− + + C , a 2 = b 2

1
a

sin − 1 at d t = t sin − 1 at +

1 − a 2 t 2 + C , a = 0

1
a

cos − 1 at d t = t cos − 1 at − 1 − a 2 t 2 + C , a = 0

1
a e at + C , a = 0

e at d t =

b at
a ln b

b at d t =

+ C , a = 0 , b > 0 , b = 1

e at
a 2

t e at d t =

( at − 1) + C , a = 0

e at
a 3 ( a 2 t 2 − 2 at + 2) + C , a = 0

t 2 e at d t =

1
a t n e at −

n
a

t n e at d t = t n − 1 e at d t , a = 0

t n b at
a ln b

n
a ln b

t n b at d t = t n − 1 b at d t , a = 0 , b > 0 , b = 1

−

e at
a 2 + b 2

e at sin bt d t = ( a sin bt − b cos bt ) + C

e at
a 2 + b 2

e at cos bt d t = ( a cos bt + b sin bt ) + C

t n + 1
n + 1 ln at −

t n + 1
( n + 1) 2

t n ln at d t = + C , n =− 1

1
t 2 + a 2 d t =

1
a

t
a

tan − 1

+ C , a = 0

t
t 2 + a 2 d t =

1
2 ln( t 2 + a 2 ) + C