What is the integral from 1 to 6 of ln(2x) ?

The integral from 1 to 6 of ln(2x) is ln(1492992)-5

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integral from 1 to 6 of ln(2x)

\int_{1}^{6} ln (2 x) d x

ln (1492992) - 5

Decimal

9.21629 \dots

Solution steps

\int_{1}^{6} ln (2 x) d x

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

6 ln (12) - 5 - ln (2)

= 6 ln (12) - 5 - ln (2)

Simplify

= ln (1492992) - 5

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\int_{- 2}^{5} 6 x - x^{2} d x

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

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What is the integral from 1 to 6 of ln(2x) ?
The integral from 1 to 6 of ln(2x) is ln(1492992)-5