What is the integral from 1 to 2 of (11)/(x^3+2x) ?

The integral from 1 to 2 of (11)/(x^3+2x) is 11/4 ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of (11)/(x^3+2x)

\int_{1}^{2} \frac{11}{x ^{3} + 2 x} d x

\frac{11}{4} ln (2)

Decimal

1.90615 \dots

Solution steps

\int_{1}^{2} \frac{11}{x ^{3} + 2 x} d x

Take the constant out:

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

= 11 \cdot \int_{1}^{2} \frac{1}{x ^{3} + 2 x} d x

Take the partial fraction of

\frac{1}{x ^{3} + 2 x} : \frac{1}{2 x} - \frac{x}{2 ( x ^{2} + 2 )}

= 11 \cdot \int_{1}^{2} \frac{1}{2 x} - \frac{x}{2 ( x ^{2} + 2 )} d x

Apply the Sum Rule:

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

= 11 (\int_{1}^{2} \frac{1}{2 x} d x - \int_{1}^{2} \frac{x}{2 ( x ^{2} + 2 )} d x)

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

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

= 11 (\frac{1}{2} ln (2) - \frac{1}{4} ln (2))

Simplify

11 (\frac{1}{2} ln (2) - \frac{1}{4} ln (2)) : \frac{11}{4} ln (2)

= \frac{11}{4} ln (2)

3 x^{2} + 2 x - 10

\frac{( 2 s + 1 )}{s ( s + 1 ) ^{2}}

y = x^{s i n (x)}

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = - 4, y^{^{'}} (0) = 0

6 x^{2} - x^{3}

What is the integral from 1 to 2 of (11)/(x^3+2x) ?
The integral from 1 to 2 of (11)/(x^3+2x) is 11/4 ln(2)