Integrate the functions in Exercises: 1 x+x - Vidyadip

Question

Integrate the functions in Exercises:
$\frac{1}{\text{x}+\text{x}\log\text{x}}$

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Answer

Putting $1 + \log \text{x}=\text{t}\ \ \ \ \ \Rightarrow\ \ \ \ \ \ \frac{1}{\text{x}}=\frac{\text{dt}}{\text{dx}}\ \ \ \ \ \Rightarrow\ \ \ \ \ \frac{\text{dx}}{\text{x}}=\text{dt} $
$\therefore\ \ \ \ \ \int \frac{1}{\text{x + x log x }}\text{ dx}$
$\int \frac{1}{\text{1 + log x }}\frac{\text{dx}}{\text{x}}==\int\frac{1}{\text{t}}\text{ dt}=\log\mid\text{t}\mid+\text{c}$
$=\log\mid\text{1+ log x}\mid+\text{ c}$

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