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

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

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integral from 1 to x of ln(t)

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

x ln (x) - x + 1

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d t = t

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

Compute the boundaries:

x ln (x) - x + 1

= x ln (x) - x + 1

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