What is the integral from 1 to 2 of (15)/(x^3+2x) ?

The integral from 1 to 2 of (15)/(x^3+2x) is 15/4 ln(2)

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integral from 1 to 2 of (15)/(x^3+2x)

\int_{1}^{2} \frac{15}{x ^{3} + 2 x} d x

\frac{15}{4} ln (2)

Decimal Notation

2.59930 \dots

Solution steps

\int_{1}^{2} \frac{15}{x ^{3} + 2 x} d x

Take the constant out:

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

= 15 \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 )}

= 15 \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

= 15 (\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)

= 15 (\frac{1}{2} ln (2) - \frac{1}{4} ln (2))

Simplify

15 (\frac{1}{2} ln (2) - \frac{1}{4} ln (2)) : \frac{15}{4} ln (2)

= \frac{15}{4} ln (2)

\frac{d}{d x} (2 x ln (x + 1))

\int \frac{( ln ( z ) ) ^{5}}{z} d z

\int e^{- 12 x} d x

x \to 5 lim (\frac{7 x}{x - 5})

y^{^{'}} + y = e^{2 x}

What is the integral from 1 to 2 of (15)/(x^3+2x) ?
The integral from 1 to 2 of (15)/(x^3+2x) is 15/4 ln(2)