What is the integral from 0 to ln(3) of x/(x^2-3x) ?

The integral from 0 to ln(3) of x/(x^2-3x) is ln(-ln(3)+3)-ln(3)

Popular >

integral from 0 to ln(3) of x/(x^2-3x)

\int_{0}^{l n (3)} \frac{x}{x ^{2} - 3 x} d x

ln (- ln (3) + 3) - ln (3)

Decimal

- 0.45602 \dots

Solution steps

\int_{0}^{l n (3)} \frac{x}{x ^{2} - 3 x} d x

Factor

\frac{x}{x ^{2} - 3 x}

= \int_{0}^{l n (3)} \frac{x}{x ( x - 3 )} d x

Cancel the common factor:

x

= \int_{0}^{l n (3)} \frac{1}{x - 3} d x

Apply u-substitution

: \int_{- 3}^{l n (3) - 3} \frac{1}{u} d u

= \int_{- 3}^{l n (3) - 3} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- 3}^{l n (3) - 3}

Compute the boundaries:

ln (- ln (3) + 3) - ln (3)

= ln (- ln (3) + 3) - ln (3)

\int_{- 1}^{1} \frac{12}{1 + x ^{2}} d x

\int_{0}^{π} \frac{7}{3} sin (x) d x

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

\int_{0}^{8} 16 x - x^{2} d x

\int_{0}^{1} sin^{3} (x) cos (x) d x

What is the integral from 0 to ln(3) of x/(x^2-3x) ?
The integral from 0 to ln(3) of x/(x^2-3x) is ln(-ln(3)+3)-ln(3)