What is the integral from 4 to 9 of ln(1+x) ?

The integral from 4 to 9 of ln(1+x) is 5ln(20)-5

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integral from 4 to 9 of ln(1+x)

\int_{4}^{9} ln (1 + x) d x

5 ln (20) - 5

Decimal

9.97866 \dots

Solution steps

\int_{4}^{9} ln (1 + x) d x

Apply u-substitution

: \int_{5}^{10} ln (u) d u

= \int_{5}^{10} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{5}^{10}

= [u ln (u) - \int 1 d u]_{5}^{10}

\int 1 d u = u

= [u ln (u) - u]_{5}^{10}

Compute the boundaries:

10 ln (10) - 5 - 5 ln (5)

= 10 ln (10) - 5 - 5 ln (5)

Simplify

= 5 ln (20) - 5

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

\int_{- 1}^{7} \frac{1}{x + 1} d x

\int_{1}^{8} 0.2 x^{2} + 1 d x

\int_{0}^{π} cos^{2} (θ) d θ

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

What is the integral from 4 to 9 of ln(1+x) ?
The integral from 4 to 9 of ln(1+x) is 5ln(20)-5