Find the undefined integral. \int \frac{1}{x(1+\ln x)}dx

khi1la2f1qv 2021-11-20 Answered
Find the undefined integral.
1x(1+lnx)dx
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Expert Answer

Witheyesse47
Answered 2021-11-21 Author has 14 answers
Step 1
Given indefinite integral 1x(1+lnx)dx.
Apply method substitution to solve the integral.
Put 1+lnx=u, then, 1xdx=du
Step 2
Then, the integral becomes,
1x(1+lnx)dx=1udu
=lnu+c
Plug in 1+lnx for u implies,
1x(1+lnx)dx=ln(1+lnx)+c
Thus, the value of integral is ln(1+lnx)+c.
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Gloria Lusk
Answered 2021-11-22 Author has 18 answers
Step 1: Use Integration by Substitution.
Let u=1+lnx,du=1xdx
Step 2: Using u and du above, rewrite 1x(1+lnx)dx.
1udu
Step 3: The derivative of lnx is 1x.
lnu
Step 4: Substitute u=1+lnx back into the original integral.
ln(1+lnx)
Step 5: Add constant.
ln(1+lnx)+C
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