Solve \(\int _{1}^{e}\frac{x\ln x}{x x\ln x}dx\)

Evaluate

\int_{1}^{e} \frac{x ln ( x )}{x \times x ln ( x )} d x

Reduce the fraction

More Steps

\int_{1}^{e} \frac{1}{x} d x

By definition,rewrite the improper integral using one-sided limit and a definite integral

a \to 1^{+} lim (\int_{a}^{e} \frac{1}{x} d x)

Evaluate the integral

More Steps

a \to 1^{+} lim (1 - ln (∣ a ∣))

Rewrite the expression

a \to 1^{+} lim (1) + a \to 1^{+} lim (- ln (∣ a ∣))

Calculate

1 + a \to 1^{+} lim (- ln (∣ a ∣))

Any expression multiplied by 0 equals 0

More Steps

1 + 0

Solution

1