What is the integral from 0 to 5 of ln(x+1) ?

The integral from 0 to 5 of ln(x+1) is 6ln(6)-5

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integral from 0 to 5 of ln(x+1)

\int_{0}^{5} ln (x + 1) d x

6 ln (6) - 5

Decimal

5.75055 \dots

Solution steps

\int_{0}^{5} ln (x + 1) d x

Apply u-substitution

: \int_{1}^{6} ln (u) d u

= \int_{1}^{6} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{1}^{6}

= [u ln (u) - \int 1 d u]_{1}^{6}

\int 1 d u = u

= [u ln (u) - u]_{1}^{6}

Compute the boundaries:

6 ln (6) - 5

= 6 ln (6) - 5

\int_{- 2}^{4} 5 d x

\int_{2}^{\infty} \frac{7}{x ^{2}} d x

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

\int_{4.9}^{5.1} x^{2} (5 x - 24.5) d x

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

What is the integral from 0 to 5 of ln(x+1) ?
The integral from 0 to 5 of ln(x+1) is 6ln(6)-5