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

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

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integral from 2 to x of ln(t)

\int_{2}^{x} ln (t) d t

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

Solution steps

\int_{2}^{x} ln (t) d t

Apply Integration By Parts

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

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

\int 1 d t = t

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

Compute the boundaries:

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

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

x = 2 y - y^{2}, x = y^{2} - 4 y

x^{2} - x, x = 4

\frac{d}{d x} (2 cos (2 x) - 1)

x \to 4 lim (x - x^{2})

\frac{d}{d y} (4 arctan (\frac{x}{y}))

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