# Sections 7.1 Basic Integration Formulas

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```					Sections 7.1:
Basic Integration Formulas
At the top of page 540 in Thomas are 22 basic integration formulae. Your
ﬁrst attempt at computing an indeﬁnite integral should be to attempt to put
the integrand into one of these forms. Then the indeﬁnite integral follows
from the formula.
Examples compute the following indeﬁnite integrals.

1.       x2 sin x3 dx.

Solution Let u = x3 , then du = 3x2 dx and we have             x2 sin x3 dx =
1                1                 1
sin u du = (− cos u) + C = − cos x3 + C.
3                3                 3
2.       sec x dx
sec x + tan x
Solution Multiply sec x by                       . We then have
sec x + tan x
sec2 x + sec x tan x
sec x dx =                          dx
sec x + tan x
d
We note that       sec x + tan x = sec2 x + sec x tan x. Thus if we let
dx
u = sec x + tan x, we have
sec2 x + sec x tan x         du
sec x dx =                           dx =       = ln |u|+C = ln | sec x+tan x|+C.
sec x + tan x             u

Be sure to read the examples on pages 540-3 and the box on the top of
page 544.

Recommended Problems
pp 544-6, # 2, 6, 7, 12, 25, 28, 29, 32, 33, 37, 40, 43, 48, 50, 53, 56, 57, 59,
63, 68, 84, 85, 87, 89, 91.

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