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

Popular >

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}

\int (- 4 x^{6} - 5 x^{5} - 2 x^{2} + 5 - e^{x}) d x

\int (x + 3) (x - 3) d x

y^{^{''}} - 2 y^{^{'}} = x + 2 e^{x}, y (0) = 17, y^{^{'}} (0) = \frac{55}{4}

\frac{1}{s ^{2} - 2 s + 26}

\frac{\partial}{\partial y} (ln (1 + x^{2} + e^{y} + z))

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