What is the integral from 5 to 13 of 1/(1+x) ?

The integral from 5 to 13 of 1/(1+x) is ln(7/3)

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integral from 5 to 13 of 1/(1+x)

\int_{5}^{13} \frac{1}{1 + x} d x

ln (\frac{7}{3})

Decimal Notation

0.84729 \dots

Solution steps

\int_{5}^{13} \frac{1}{1 + x} d x

Apply u-substitution

: \int_{6}^{14} \frac{1}{u} d u

= \int_{6}^{14} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{6}^{14}

Compute the boundaries:

ln (14) - ln (6)

= ln (14) - ln (6)

Simplify

= ln (\frac{7}{3})

\int_{6}^{\infty} \frac{ln ( x )}{x} d x

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

2 x^{2} + x

\int \frac{8 x ^{2}}{( 1 - x ^{3} ) ^{3}} d x

\int \frac{x ^{4} - 5 x}{x ^{2}} d x

What is the integral from 5 to 13 of 1/(1+x) ?
The integral from 5 to 13 of 1/(1+x) is ln(7/3)