What is the integral from 5 to 2x of ln(u) ?

The integral from 5 to 2x of ln(u) is 2xln(2x)-2x-5ln(5)+5

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integral from 5 to 2x of ln(u)

\int_{5}^{2 x} ln (u) d u

2 x ln (2 x) - 2 x - 5 ln (5) + 5

Solution steps

\int_{5}^{2 x} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{5}^{2 x}

= [u ln (u) - \int 1 d u]_{5}^{2 x}

\int 1 d u = u

= [u ln (u) - u]_{5}^{2 x}

Compute the boundaries:

2 x ln (2 x) - 2 x - 5 ln (5) + 5

= 2 x ln (2 x) - 2 x - 5 ln (5) + 5

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What is the integral from 5 to 2x of ln(u) ?
The integral from 5 to 2x of ln(u) is 2xln(2x)-2x-5ln(5)+5