What is the integral from 2 to 4 of ln(x+1) ?

The integral from 2 to 4 of ln(x+1) is 5ln(5)-2-3ln(3)

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integral from 2 to 4 of ln(x+1)

\int_{2}^{4} ln (x + 1) d x

5 ln (5) - 2 - 3 ln (3)

Decimal

2.75135 \dots

Solution steps

\int_{2}^{4} ln (x + 1) d x

Apply u-substitution

: \int_{3}^{5} ln (u) d u

= \int_{3}^{5} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{3}^{5}

= [u ln (u) - \int 1 d u]_{3}^{5}

\int 1 d u = u

= [u ln (u) - u]_{3}^{5}

Compute the boundaries:

5 ln (5) - 2 - 3 ln (3)

= 5 ln (5) - 2 - 3 ln (3)

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

\int_{1}^{3} \frac{1}{4 x - x ^{2}} d x

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\int_{1}^{2} ln (3 x) - ln (x) d x

\int_{0}^{π} 9 sin (x) - sin (9 x) d x

What is the integral from 2 to 4 of ln(x+1) ?
The integral from 2 to 4 of ln(x+1) is 5ln(5)-2-3ln(3)