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

The integral from 2 to 3 of (x^3+2)/(x^4) is ln(3)-ln(2)+19/324

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integral from 2 to 3 of (x^3+2)/(x^4)

\int_{2}^{3} \frac{x ^{3} + 2}{x ^{4}} d x

ln (3) - ln (2) + \frac{19}{324}

Decimal

0.46410 \dots

Solution steps

\int_{2}^{3} \frac{x ^{3} + 2}{x ^{4}} d x

Expand

\frac{x ^{3} + 2}{x ^{4}} : \frac{1}{x} + \frac{2}{x ^{4}}

= \int_{2}^{3} \frac{1}{x} + \frac{2}{x ^{4}} 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

= \int_{2}^{3} \frac{1}{x} d x + \int_{2}^{3} \frac{2}{x ^{4}} d x

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

\int_{2}^{3} \frac{2}{x ^{4}} d x = \frac{19}{324}

= ln (3) - ln (2) + \frac{19}{324}

What is the integral from 2 to 3 of (x^3+2)/(x^4) ?
The integral from 2 to 3 of (x^3+2)/(x^4) is ln(3)-ln(2)+19/324