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

The integral from-1 to 1 of (x^2)/(x+2) is 4ln(3)-4

Popular >

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

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

4 ln (3) - 4

Decimal Notation

0.39444 \dots

Solution steps

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

Apply u-substitution

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

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

Expand

\frac{( u - 2 ) ^{2}}{u} : u - 4 + \frac{4}{u}

= \int_{1}^{3} u - 4 + \frac{4}{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 d u - \int_{1}^{3} 4 d u + \int_{1}^{3} \frac{4}{u} d u

\int_{1}^{3} u d u = 4

\int_{1}^{3} 4 d u = 8

\int_{1}^{3} \frac{4}{u} d u = 4 ln (3)

= 4 - 8 + 4 ln (3)

Simplify

= 4 ln (3) - 4

\int_{- 1}^{1} 1 3^{x} d x

\int_{- \infty}^{- 1} \frac{1}{x ^{5}} d x

\int_{2}^{4} \frac{1}{x ln ^{2} ( x )} d x

\int_{0}^{\infty} \frac{1}{y ^{3}} d y

\int_{1}^{100 e} \frac{1}{x} - 5 d x

What is the integral from-1 to 1 of (x^2)/(x+2) ?
The integral from-1 to 1 of (x^2)/(x+2) is 4ln(3)-4