54. Using different substitutions Show that the integral Jur - 1)(x + 1))~2dx can be evaluated with any of the following substitutions. a. u = 1/(x + 1) b. u = ((x - 1)/(x + 1)) for k = 1, 1/2, 1/3, -1/3, -2/3, and -1 d. u = tan- V f. u = cos-x c. u = tan-' x e. u = tan- ((x - 1)/2) g. u = cosh¬!x What is the value of the integral?

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Chapter1: Functions And Models
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54. Using different substitutions
Show that the integral
Jur -
1)(x + 1))~2dx
can be evaluated with any of the following substitutions.
a. u = 1/(x + 1)
b. u = ((x - 1)/(x + 1)) for k = 1, 1/2, 1/3, -1/3, -2/3,
and -1
d. u = tan- V
f. u = cos-x
c. u = tan-' x
e. u = tan- ((x - 1)/2)
g. u = cosh¬!x
What is the value of the integral?
Transcribed Image Text:54. Using different substitutions Show that the integral Jur - 1)(x + 1))~2dx can be evaluated with any of the following substitutions. a. u = 1/(x + 1) b. u = ((x - 1)/(x + 1)) for k = 1, 1/2, 1/3, -1/3, -2/3, and -1 d. u = tan- V f. u = cos-x c. u = tan-' x e. u = tan- ((x - 1)/2) g. u = cosh¬!x What is the value of the integral?
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