Make the u-substitution 2 sin x = 2u 1+u²' COS X 1- u² 1+ u² and dx = du 1+u² to convert the integrand to a rational function of u, and then evaluate the integral. If you have a CAS, use it to evaluate the integral (no substitution), and then confirm that the results are equivalent. 1 1₂ dx + C 24 sin x 7 cos x

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 29EQ
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Make the u-substitution
2u
2
sin x
1- u²
1+ u²
COS X =
and
dx
=
-
du
1+u²⁹
+ u²
to convert the integrand to a rational function of u, and then
evaluate the integral. If you have a CAS, use it to evaluate the
integral (no substitution), and then confirm that the results are
equivalent.
1
S
dx
+C
24 sin x 7 cos x
Transcribed Image Text:Make the u-substitution 2u 2 sin x 1- u² 1+ u² COS X = and dx = - du 1+u²⁹ + u² to convert the integrand to a rational function of u, and then evaluate the integral. If you have a CAS, use it to evaluate the integral (no substitution), and then confirm that the results are equivalent. 1 S dx +C 24 sin x 7 cos x
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