Evaluate the following integrals. \int \frac{1}{x+\sqrt{x}}dx

he298c 2021-10-20 Answered
Evaluate the following integrals.
1x+xdx
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Expert Answer

toroztatG
Answered 2021-10-21 Author has 98 answers
Step 1
Consider the integral:
1x+xdx
Apply u−substitution:
u=x
1x+xdx=2u+1du
Take the constant out:
2u+1du=21u+1du
Let v=u+1
=21vdv
=2ln|v|+C
=2ln|u+1|+C
=2ln|x+1|+C
Step 2
Hence:
1x+xdx=2ln|x+1|+C
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