What is the integral from e to e^2 of ln(x) ?

The integral from e to e^2 of ln(x) is e^2

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integral from e to e^2 of ln(x)

\int_{e}^{e^{2}} ln (x) d x

e^{2}

Decimal

7.38905 \dots

Solution steps

\int_{e}^{e^{2}} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{e}^{e^{2}}

= [x ln (x) - \int 1 d x]_{e}^{e^{2}}

\int 1 d x = x

= [x ln (x) - x]_{e}^{e^{2}}

Compute the boundaries:

e^{2}

= e^{2}

x \to 3 lim (\frac{( 9 - x ^{2} )}{cos ( \frac{π}{2} x )})

n = 0 \sum \infty (- 1)^{2 n + 1}

\int sin^{2} (θ) cos^{2} (θ) d θ

\int \frac{1}{1 + 6 x} d x

\frac{d}{d x} ((x^{2} + 2)^{2} (x^{4} + 4)^{4})

What is the integral from e to e^2 of ln(x) ?
The integral from e to e^2 of ln(x) is e^2