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

The integral from 1 to 3 of x^2+1/(4x^2) is 53/6

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integral from 1 to 3 of x^2+1/(4x^2)

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

\frac{53}{6}

Decimal

8.83333 \dots

Solution steps

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

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} \frac{1}{4 x ^{2}} d x = \frac{1}{6}

= \frac{26}{3} + \frac{1}{6}

Simplify

\frac{26}{3} + \frac{1}{6} : \frac{53}{6}

= \frac{53}{6}

What is the integral from 1 to 3 of x^2+1/(4x^2) ?
The integral from 1 to 3 of x^2+1/(4x^2) is 53/6