For Exercises 55-56, find the partial fraction decomposition for the given expression. [Hint. Use the substitution u = e x and recall that e 2 x = e x 2 . ] 5 e x + 7 e 2 x + 3 e x + 2
For Exercises 55-56, find the partial fraction decomposition for the given expression. [Hint. Use the substitution u = e x and recall that e 2 x = e x 2 . ] 5 e x + 7 e 2 x + 3 e x + 2
Solution Summary: The author explains the partial tion decomposition for the given expression 5ex+7 e x. Substitute the denominator of the rational tion
For Exercises 55-56, find the partial fraction decomposition for the given expression. [Hint. Use the substitution
u
=
e
x
and recall that
e
2
x
=
e
x
2
.
]
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
Find the indefinite integral by making a change of variables. (Remember the constant of integration.)
√(x+4)
4)√6-x dx
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