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

The integral from 1 to 3x of ln(t) is 3xln(3x)-3x+1

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integral from 1 to 3x of ln(t)

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

3 x ln (3 x) - 3 x + 1

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d t = t

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

Compute the boundaries:

3 x ln (3 x) - 3 x + 1

= 3 x ln (3 x) - 3 x + 1

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