Integration Rules
1.\,\int k\,\text{d}x = kx +c
2.\,\int x^n\,\text{d}x = \dfrac{x^{n+1}}{n+1} +c, n\ne -1
3.\,\int \sin x\,\text{d}x = -\cos x +c
4.\,\int \cos x\,\text{d}x = \sin x +c
5.\,\int \sec^2 x\,\text{d}x = \tan x +c
6.\,\int e^x\,\text{d}x = e^x +c
7.\,\int \frac{1}{x}\,\text{d}x = \ln x +c
Note: \int k\text{f}(x)\,\text{d}x=k\times\int \text{f}(x)\,\text{d}x
Further Integration Rules
1.\,\int (ax+b)^n\,\text{d}x = \dfrac{(ax+b)^{n+1}}{a(n+1)} +c, n \ne -1\$2.\,\int \sin (ax+b)\,\text{d}x = -\dfrac{\cos (ax+b)}{a} +c\$
3.\,\int \cos (ax+b)\,\text{d}x = \dfrac{\sin (ax+b)}{a} +c\$4.\,\int \sec^2 (ax+b)\,\text{d}x = \dfrac{\tan (ax+b)}{a} +c\$
5.\,\int e^{ax+b}\,\text{d}x = \dfrac{e^{ax+b}}{a} +c\$6.\,\int \frac{1}{ax+b}\,\text{d}x = \dfrac{\ln (ax+b)}{a}+c[/stextbox]  [stextbox caption="Definite Integral" stextbox id="info"]For\int \text{f}(x) \,\text{d}x = \text{F}(x) + c,\displaystyle\int_a^b \text{f}(x) \,\text{d}x = \text{F}(b) -\text{F}(a).[/stextbox]  [stextbox caption="Area With Respect Tox-axis Ory-axis" stextbox id="default"]For area with respect tox-axis,\displaystyle\int_a^b \text{f}(x) \,\text{d}x. For area with respect toy-axis,\displaystyle\int_c^d \text{f}(y) \,\text{d}y. Note: For area below thex-axis (taken with respect tox-axis) or area to the left of they-axis (taken with respect toy-axis), it is taken as negative. [/stextbox]  [stextbox caption="Kinematics" stextbox id="download"]1.\,v=\dfrac{\text{d}s}{\text{d}t}\$
2.\,a=\dfrac{\text{d}v}{\text{d}t}\$3.\,s=\displaystyle\int v\,\text{d}t\$
4.\,v=\displaystyle\int a\,\text{d}t

a. velocity, v determines both the speed and the direction
b. \text{average speed}=\dfrac{\text{total distance}}{\text{total time}}
c. particle starts from origin, s = 0
d. instantaneously at rest, v = 0
e. max / min velocity, a=\dfrac{\text{d}v}{\text{d}t}=0
f. max / min displacement, v=\dfrac{\text{d}s}{\text{d}t}=0