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

The integral from 0 to pi of ln(x) is piln(pi)-pi

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integral from 0 to pi of ln(x)

\int_{0}^{π} ln (x) d x

π ln (π) - π

Decimal Notation

0.45468 \dots

Solution steps

\int_{0}^{π} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{π}

= [x ln (x) - \int 1 d x]_{0}^{π}

\int 1 d x = x

= [x ln (x) - x]_{0}^{π}

Compute the boundaries:

π ln (π) - π

= π ln (π) - π

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

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x))^{3} d x

\int_{0}^{1} 1 + \frac{9}{4} y d y

\int_{1}^{3} x^{5} x^{6} - 1 d x

\int_{0}^{\frac{π}{3}} 6 x sin (x) d x

What is the integral from 0 to pi of ln(x) ?
The integral from 0 to pi of ln(x) is piln(pi)-pi