Chloe W.

asked • 04/22/16

Integration by Substitution

Find using substitution:
 
∫ 1/[x(1+lnx)2] dx
 
I'm not sure what substitution to use. 

Matthew D.

Yup. good job.
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04/23/16

1 Expert Answer

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Matthew D. answered • 04/22/16

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 Use U substitution 
 
u = 1+ lnx  take derivative
du = 1/x dx
 
∫U-2du notice that du = 1/x dx. and U-2 is just another way of writing 1/U2
 
take anti-derivative
 
-U-1 +C
-1/(1+lnx) +C
 
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Michael J.

I do not think this will work because (x(1 + lnx)) is being the squared.  The factor, x, is not isolated.
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04/23/16

Michael J.

Nevermind my comment.  I had thought the denominator term was being squared.  Only the (1 + lnx) term is being squared.
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04/23/16

Chloe W.

Thank you. I got
-1 /[1+lnx] + c
 
Is that the answer?
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04/23/16

Matthew D.

yup, good job.
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04/23/16

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