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

Find the undefined integral.
$\int \frac{1}{x\left(1+\mathrm{ln}x\right)}dx$
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Witheyesse47
Step 1
Given indefinite integral $\int \frac{1}{x\left(1+\mathrm{ln}x\right)}dx$.
Apply method substitution to solve the integral.
Put
Step 2
Then, the integral becomes,
$\int \frac{1}{x\left(1+\mathrm{ln}x\right)}dx=\int \frac{1}{u}du$
$=\mathrm{ln}u+c$
Plug in $1+\mathrm{ln}x$ for u implies,
$\int \frac{1}{x\left(1+\mathrm{ln}x\right)}dx=\mathrm{ln}\left(1+\mathrm{ln}x\right)+c$
Thus, the value of integral is $\mathrm{ln}\left(1+\mathrm{ln}x\right)+c$.
###### Not exactly what you’re looking for?
Gloria Lusk
Step 1: Use Integration by Substitution.
Let $u=1+\mathrm{ln}x,du=\frac{1}{x}dx$
Step 2: Using u and du above, rewrite $\int \frac{1}{x\left(1+\mathrm{ln}x\right)}dx$.
$\int \frac{1}{u}du$
Step 3: The derivative of .
$\mathrm{ln}u$
Step 4: Substitute $u=1+\mathrm{ln}x$ back into the original integral.
$\mathrm{ln}\left(1+\mathrm{ln}x\right)$
$\mathrm{ln}\left(1+\mathrm{ln}x\right)+C$