What is the integral from 1 to 2 of (x^2)/(x^3+2) ?

The integral from 1 to 2 of (x^2)/(x^3+2) is 1/3 (ln(10)-ln(3))

Popular >

integral from 1 to 2 of (x^2)/(x^3+2)

\int_{1}^{2} \frac{x ^{2}}{x ^{3} + 2} d x

\frac{1}{3} (ln (10) - ln (3))

Decimal

0.40132 \dots

Solution steps

\int_{1}^{2} \frac{x ^{2}}{x ^{3} + 2} d x

Apply u-substitution

: \int_{3}^{10} \frac{1}{3 u} d u

= \int_{3}^{10} \frac{1}{3 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{3}^{10} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{3}^{10}

Compute the boundaries:

ln (10) - ln (3)

= \frac{1}{3} (ln (10) - ln (3))

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

\int_{0.5}^{1} (2 - 2 x) d x

\int_{x^{1}}^{x^{2}} 1 d x

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

\int_{0}^{\infty} e^{- b x^{2}} d x

What is the integral from 1 to 2 of (x^2)/(x^3+2) ?
The integral from 1 to 2 of (x^2)/(x^3+2) is 1/3 (ln(10)-ln(3))