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# 4 - |-23 ln x 27 1 Prob 15 The integral is improper because...

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Solution set for Math 155, of Assignment 4 Prob. 1 3 4 . Prob. 2 1 . Prob. 3 1 2 ln ln 5 ln 2 . Prob. 4 1 3 x 3 ln x - x 3 9 , ( u = ln x , v = x 2 ) . Prob. 5 2 , ( u = ln x 2 , v = 1 ) . Prob. 6 1 4 ( - 2 + ( 3 + 1 ) e π/ 6 , ( u = cos x , v = e x ) ,u = sin x , v = e x . Prob. 7 - 2 17 cos x 2 + 4 sin x 2 , ( u = sin x 2 , v = e - 2 x ) , ( u = 1 2 cos x 2 , v = - e - 2 x 2 ) . Prob. 8 We have arccos xdx = x arccos x + x 1 - x 2 dx = x arccos x + - 1 2 u du ( 1 - x 2 = u ) = x arccos x - u = x arccos x - 1 - x 2 . Prob. 9 1 3 arctan x 3 , ( x 3 = y ) . Prob. 10 ln 16 - 1 2 . Prob. 11 ln | ( x - 3 )( x + 2 ) | . Prob. 12 2 7 arctan 2 x - 1 7 . Prob. 13 - 1 2 ln 3 2 . Prob. 14 5 9 x - 1

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Unformatted text preview: | -23 ln x 27 . 1 Prob. 15 The integral is improper because it has inﬁnite upper limit. Its value is 1 . Prob. 16 The integral is improper because it has inﬁnite limits. Its value is . Prob. 17 The integral is convergent. Its value is 3 π 4 . 2...
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