Integration Rules

Integration Integration can be used to find areas, volumes, central points and many useful things. But it is often used to find the area underneath the graph of a function like this:

The integral of many functions are well known, and there are useful rules to work out the integral of more complicated functions, many of which are shown here.

There are examples below to help you.

Common Functions	Function	Integral
Constant	∫a dx	ax + C
Variable	∫x dx	x2/2 + C
Square	∫x2 dx	x3/3 + C
Reciprocal	∫(1/x) dx	ln|x| + C
Exponential	∫ex dx	ex + C
	∫ax dx	ax/ln(a) + C
	∫ln(x) dx	x ln(x) − x + C
Trigonometry (x in radians)	∫cos(x) dx	sin(x) + C
	∫sin(x) dx	-cos(x) + C
	∫sec2(x) dx	tan(x) + C
Rules	Function	Integral
Multiplication by constant	∫cf(x) dx	c∫f(x) dx
Power Rule (n≠-1)	∫xn dx	xn+1n+1 + C
Sum Rule	∫(f + g) dx	∫f dx + ∫g dx
Difference Rule	∫(f - g) dx	∫f dx - ∫g dx
Integration by Parts	See Integration by Parts
Substitution Rule	See Integration by Substitution