What is the integral from 3 to 4 of ln(x^3-2x^2) ?

The integral from 3 to 4 of ln(x^3-2x^2) is 18ln(2)-3-6ln(3)

integral from 3 to 4 of ln(x^3-2x^2)

\int_{3}^{4} ln (x^{3} - 2 x^{2}) d x

18 ln (2) - 3 - 6 ln (3)

Decimal

2.88497 \dots

Solution steps

\int_{3}^{4} ln (x^{3} - 2 x^{2}) d x

Apply Integration By Parts

= [x ln (x^{3} - 2 x^{2}) - \int \frac{3 x - 4}{x - 2} d x]_{3}^{4}

\int \frac{3 x - 4}{x - 2} d x = 3 x - 6 + 2 ln ∣ x - 2 ∣

= [x ln (x^{3} - 2 x^{2}) - (3 x - 6 + 2 ln ∣ x - 2 ∣)]_{3}^{4}

Simplify

= [x ln (x^{3} - 2 x^{2}) - 3 x + 6 - 2 ln ∣ x - 2 ∣]_{3}^{4}

Compute the boundaries:

18 ln (2) - 3 - 6 ln (3)

= 18 ln (2) - 3 - 6 ln (3)

\int_{1}^{6} \frac{7}{x} d x

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

\int_{5}^{6} \frac{6}{x ^{2}} d x

\int_{0}^{1} 2 π x (3 x (x - 2)^{2}) d x

\int_{- 2}^{2} (- x^{2} - 4) d x

What is the integral from 3 to 4 of ln(x^3-2x^2) ?
The integral from 3 to 4 of ln(x^3-2x^2) is 18ln(2)-3-6ln(3)