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

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

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integral from 1 to 2 of ln(2x)

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

3 ln (2) - 1

Decimal

1.07944 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

3 ln (2) - 1

= 3 ln (2) - 1

\int_{- l}^{0} (x + l) d x

\int_{0}^{4} \frac{1}{1 + t} d t

\int_{0}^{2} - 2 x^{3} + 8 x d x

\int_{0}^{\frac{y}{3}} \frac{y ^{2} - 9 x ^{2}}{2} d x

\int_{2}^{4} \frac{2}{x ^{2} + x - 2} d x

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