What is the integral from 0 to 3 of ln(x+1) ?

The integral from 0 to 3 of ln(x+1) is 8ln(2)-3

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integral from 0 to 3 of ln(x+1)

\int_{0}^{3} ln (x + 1) d x

8 ln (2) - 3

Decimal Notation

2.54517 \dots

Solution steps

\int_{0}^{3} ln (x + 1) d x

Apply u-substitution

: \int_{1}^{4} ln (u) d u

= \int_{1}^{4} ln (u) d u

Apply Integration By Parts

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

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

\int 1 d u = u

= [u ln (u) - u]_{1}^{4}

Compute the boundaries:

8 ln (2) - 3

= 8 ln (2) - 3

\int (1 - x)^{n} d x

n = 0 \sum \infty e^{- 5 n}

\int_{0}^{2} 0.09375 (4 - x^{2}) d x

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What is the integral from 0 to 3 of ln(x+1) ?
The integral from 0 to 3 of ln(x+1) is 8ln(2)-3