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

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

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integral from 1 to x of ln(x)

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

x ln (x) - x + 1

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

x ln (x) - x + 1

= x ln (x) - x + 1

\int_{- 1}^{0} 9 x^{2} (2 x^{3} + 5)^{2} d x

\int_{1}^{2} \frac{v ^{4} + 3 v ^{7}}{v ^{5}} d v

\int_{0}^{2 π} 2 sin (x) d x

\int_{0}^{8.12} 1000 x + 250 d x

\int_{1}^{4} x^{- 5} d x

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