What is the integral from 1 to 3 of ln(2x) ?

The integral from 1 to 3 of ln(2x) is ln(108)-2

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integral from 1 to 3 of ln(2x)

\int_{1}^{3} ln (2 x) d x

ln (108) - 2

Decimal Notation

2.68213 \dots

Solution steps

\int_{1}^{3} ln (2 x) d x

Apply Integration By Parts

: [x ln (2 x) - \int 1 d x]_{1}^{3}

= [x ln (2 x) - \int 1 d x]_{1}^{3}

\int 1 d x = x

= [x ln (2 x) - x]_{1}^{3}

Compute the boundaries:

3 ln (6) - 2 - ln (2)

= 3 ln (6) - 2 - ln (2)

Simplify

= ln (108) - 2

x \to π lim (5)

f (x) = x sec (x)

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

cos (x)

x \to 0 lim (x^{2} - sin (\frac{1}{x}))

What is the integral from 1 to 3 of ln(2x) ?
The integral from 1 to 3 of ln(2x) is ln(108)-2