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

The integral from-1 to 1 of (x^3)/(x+2) is 26/3-8ln(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{26}{3} - 8 ln (3)

Decimal

- 0.12223 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{3} \frac{( u - 2 ) ^{3}}{u} d u

= \int_{1}^{3} \frac{( u - 2 ) ^{3}}{u} d u

Expand

\frac{( u - 2 ) ^{3}}{u} : u^{2} - 6 u + 12 - \frac{8}{u}

= \int_{1}^{3} u^{2} - 6 u + 12 - \frac{8}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} u^{2} d u - \int_{1}^{3} 6 u d u + \int_{1}^{3} 12 d u - \int_{1}^{3} \frac{8}{u} d u

\int_{1}^{3} u^{2} d u = \frac{26}{3}

\int_{1}^{3} 6 u d u = 24

\int_{1}^{3} 12 d u = 24

\int_{1}^{3} \frac{8}{u} d u = 8 ln (3)

= \frac{26}{3} - 24 + 24 - 8 ln (3)

Simplify

= \frac{26}{3} - 8 ln (3)

\int_{0}^{0.35} ln (1 + x^{2}) d x

\int_{π}^{\frac{3 π}{2}} (x sin (x)) d x

\int_{0}^{l} x^{2} d x

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

\int_{0}^{2 π} 2 sin (t) d t

What is the integral from-1 to 1 of (x^3)/(x+2) ?
The integral from-1 to 1 of (x^3)/(x+2) is 26/3-8ln(3)