What is the integral from 2 to 6 of ln(x) ?

The integral from 2 to 6 of ln(x) is 2ln(108)-4

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integral from 2 to 6 of ln(x)

\int_{2}^{6} ln (x) d x

2 ln (108) - 4

Decimal Notation

5.36426 \dots

Solution steps

\int_{2}^{6} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{2}^{6}

= [x ln (x) - \int 1 d x]_{2}^{6}

\int 1 d x = x

= [x ln (x) - x]_{2}^{6}

Compute the boundaries:

6 ln (6) - 4 - 2 ln (2)

= 6 ln (6) - 4 - 2 ln (2)

Simplify

= 2 ln (108) - 4

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

f (x) = sin (sin (x)), at x = (4 π)

\int cos (2 x) + 1 d x

\int 3 e^{2 t} d t

What is the integral from 2 to 6 of ln(x) ?
The integral from 2 to 6 of ln(x) is 2ln(108)-4