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

The integral from 1 to 2 of (1+x^2)/(x^4) is 19/24

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integral from 1 to 2 of (1+x^2)/(x^4)

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

\frac{19}{24}

Decimal

0.79166 \dots

Solution steps

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

Expand

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

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

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

\int_{1}^{2} \frac{1}{x ^{4}} d x = \frac{7}{24}

\int_{1}^{2} \frac{1}{x ^{2}} d x = \frac{1}{2}

= \frac{7}{24} + \frac{1}{2}

Simplify

\frac{7}{24} + \frac{1}{2} : \frac{19}{24}

= \frac{19}{24}

What is the integral from 1 to 2 of (1+x^2)/(x^4) ?
The integral from 1 to 2 of (1+x^2)/(x^4) is 19/24