What is the integral from 0 to x of ln(t) ?

The integral from 0 to x of ln(t) is xln(x)-x

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integral from 0 to x of ln(t)

\int_{0}^{x} ln (t) d t

x ln (x) - x

Solution steps

\int_{0}^{x} ln (t) d t

Apply Integration By Parts

: [t ln (t) - \int 1 d t]_{0}^{x}

= [t ln (t) - \int 1 d t]_{0}^{x}

\int 1 d t = t

= [t ln (t) - t]_{0}^{x}

Compute the boundaries:

x ln (x) - x

= x ln (x) - x

\int_{0}^{x} \frac{y}{x} d y

\int_{0}^{y} cos (1 0^{6} t - 2 y) d y

\int_{1}^{3} (1 + 2 x) d x

\int_{1}^{x} t d t

\int_{0}^{x^{2}} cos (t^{4}) d t

What is the integral from 0 to x of ln(t) ?
The integral from 0 to x of ln(t) is xln(x)-x