Page 8 - LAPLACE TRANSFORM

Basic Integration Rules

3
∫ (1) dt = t + C t2 2
1/2
3/2
∫ √t dt = ∫ t = 3 = t + C
2 3
∫ (10) dt = 10t + C
1
at
at
∫ e dt = e + C
2

∫t dt = + C
2
1
-at
-at
3

2
∫t dt = + C ∫ e dt = e + C
−
3
1
2t
2t

∫ dt = + C ∫ e dt = e + C

2
∫cos(t) dt = sin(t) + C -2t 1 -2t
∫ e dt = e + C
−2
1
∫cos(2t) dt = sin(2t) + C
2
2
t
∫ 8tdt = 8 = 4 t + C
2
∫sin(t) dt = − cos(t) + C 2
3
1
t
3
2
∫sin(2t) dt = − cos(2t) + C ∫ 6t dt = 6 = 2 t + C
2 3
1
∫ dt = In t + C 4 t 5 5
∫ 5t dx = 5 = t + C
5

Exponent Rules

0
Zero rule e = 1

∞
Limits at infinity e = 0

2