What is the integral from 0 to 4 of ln(x) ?

The integral from 0 to 4 of ln(x) is 8ln(2)-4

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integral from 0 to 4 of ln(x)

\int_{0}^{4} ln (x) d x

8 ln (2) - 4

Decimal Notation

1.54517 \dots

Solution steps

\int_{0}^{4} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{4}

= [x ln (x) - \int 1 d x]_{0}^{4}

\int 1 d x = x

= [x ln (x) - x]_{0}^{4}

Compute the boundaries:

8 ln (2) - 4

= 8 ln (2) - 4

\int_{0}^{1 - x} 2 d y

\int_{- 2}^{4} x^{2} - 2 x - 8 d x

\int_{0}^{1} \frac{1}{( 1 + x ^{2} )} d x

\int_{0}^{8} \frac{1}{x ^{2} + 64} d x

\int_{0}^{t} e^{- t} d t

What is the integral from 0 to 4 of ln(x) ?
The integral from 0 to 4 of ln(x) is 8ln(2)-4