Question
Evaluate: $\int_e^{e^2} \frac{d x}{x \log x}$
✓
Answer
Put log(x) = t
or $d t=\frac{1}{x} d x$
Put $x=e^2$ or $t=2$ and $x=e$ or $t=1$
$\therefore \quad \int_c^{c^2} \frac{d x}{x \log x}=\int_1^2 \frac{d t}{t}$
= log(2) - log(1)
= log(2)
or $d t=\frac{1}{x} d x$
Put $x=e^2$ or $t=2$ and $x=e$ or $t=1$
$\therefore \quad \int_c^{c^2} \frac{d x}{x \log x}=\int_1^2 \frac{d t}{t}$
= log(2) - log(1)
= log(2)
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