What is the integral from 1 to infinity of 1/(x+x^2) ?

The integral from 1 to infinity of 1/(x+x^2) is ln(2)

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integral from 1 to infinity of 1/(x+x^2)

\int_{1}^{\infty} \frac{1}{x + x ^{2}} d x

ln (2)

Decimal

0.69314 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{x + x ^{2}} d x

Compute the indefinite integral:

\int \frac{1}{x + x ^{2}} d x = ln ∣ x ∣ - ln ∣ x + 1 ∣ + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x + x ^{2}} d x = 0 - (- ln (2))

= 0 - (- ln (2))

Simplify

= ln (2)

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What is the integral from 1 to infinity of 1/(x+x^2) ?
The integral from 1 to infinity of 1/(x+x^2) is ln(2)