Tuesday, June 21, 2016

calculus - Solving the improper integral intinfty0fracdx1+x3



0dx1+x3



So far I have found the indefinite integral, which is:



16ln|x2x+1|+13arctan(2x13)+13ln|x+1|




Now what do I need to do in order to calculate the improper integral?


Answer



Next, simplify
F(x)=16ln|x2x+1|+13arctan2x13+13ln|x+1|


=13arctan(2x13)+13ln|x+1|13ln|x2x+1|

=13arctan(2x13)+13ln(|x+1||x2x+1|).

Then
0dx1+x3=limXF(X)F(0).

Compute the limit, and you are done.


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