What is the integral from 1 to 13 of ln(t) ?

The integral from 1 to 13 of ln(t) is 13ln(13)-12

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integral from 1 to 13 of ln(t)

\int_{1}^{13} ln (t) d t

13 ln (13) - 12

Decimal

21.34434 \dots

Solution steps

\int_{1}^{13} ln (t) d t

Apply Integration By Parts

: [t ln (t) - \int 1 d t]_{1}^{13}

= [t ln (t) - \int 1 d t]_{1}^{13}

\int 1 d t = t

= [t ln (t) - t]_{1}^{13}

Compute the boundaries:

13 ln (13) - 12

= 13 ln (13) - 12

\int_{0}^{3} x^{5} d x

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

\int_{3}^{11} x^{2} d x

\int_{1}^{2} x x^{2} + 1 d x

\int_{2}^{5} \frac{1}{x ^{2} - 4 x + 13} d x

What is the integral from 1 to 13 of ln(t) ?
The integral from 1 to 13 of ln(t) is 13ln(13)-12