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

The integral from 1 to 2 of (x^2+1/(4x^2)) is 59/24

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

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

\frac{59}{24}

Decimal Notation

2.45833 \dots

Solution steps

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} \frac{1}{4 x ^{2}} d x = \frac{1}{8}

= \frac{7}{3} + \frac{1}{8}

Simplify

\frac{7}{3} + \frac{1}{8} : \frac{59}{24}

= \frac{59}{24}

\int \frac{y}{2 x + 3 y} d x

\frac{d}{d x} (x^{2} e^{x} cos (2 x))

\frac{d}{d x} (- 6 cot (x) csc (x))

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

(7.2) (2.8)

What is the integral from 1 to 2 of (x^2+1/(4x^2)) ?
The integral from 1 to 2 of (x^2+1/(4x^2)) is 59/24