Integration by Standard Form

Exercises for students
Integrate the following with respect to x and check your working using the above applet:

(3x + 4)2	(3x + 4)-2	(3x + 4)-1	(3x + 4)1/2
(3x + 4)-1/2	(3x + 4)3/2	ex+3	e2x
sin (2x)	cos (2x)	tan (2x)	sec2 (3x + 4)
1 / sqrt(4 - x2)	1 / sqrt(1 - 9x2)	1 / sqrt(4 - 9x2)
1 / (4 + x2)	1 / (1 + 9x2)	1 / (4 + 9x2)

Summary

∫ (ax + b)n dx =	1	(ax + b)n+1	+ c       if n not = -1
	_	_________
	a	n + 1

∫	1	dx =	1	ln | ax + b |	+ c
	ax + b		a

∫ eax+b dx =	eax+b	+ c
	_____
	a

∫ sin (ax+b) dx =	- cos (ax+b)	+ c		∫ cos (ax+b) dx =	sin (ax+b)	+ c
	a				a

∫ sin2 x dx =	1	∫ 1 - cos 2x dx		∫ cos2 x dx =	1	∫ 1 + cos 2x dx
	2				2

∫ sec2 (ax+b) dx =	tan (ax+b)	+ c		∫ cosec2 (ax+b) dx =	- cot (ax+b)	+ c
	a				a

∫ tan2 x dx = ∫ sec2 x - 1 dx		∫ cot2 x dx = ∫ cosec2 x - 1 dx
∫ tan x dx = - ln | cos x | + c		∫ cot x dx = ln | sin x | + c
∫ sec x dx = ln | sec x + tan x | + c		∫ cosec x dx = - ln | cosec x + cot x | + c

∫ ax dx =	ax	+ c
	___
	ln a

∫

1

dx =

sin-1

x

+ c

∫

1

dx =

1

tan-1

x

+ c

sqrt ( a2 - x2 )

a

a2 + x2

a

a

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