What is the integral from 6 to 8 of ((x^2+6)/(x^2)) ?

The integral from 6 to 8 of ((x^2+6)/(x^2)) is 9/4

Popular >

integral from 6 to 8 of ((x^2+6)/(x^2))

\int_{6}^{8} (\frac{x ^{2} + 6}{x ^{2}}) d x

\frac{9}{4}

Decimal Notation

2.25

Solution steps

\int_{6}^{8} \frac{x ^{2} + 6}{x ^{2}} d x

Expand

\frac{x ^{2} + 6}{x ^{2}} : 1 + \frac{6}{x ^{2}}

= \int_{6}^{8} 1 + \frac{6}{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_{6}^{8} 1 d x + \int_{6}^{8} \frac{6}{x ^{2}} d x

\int_{6}^{8} 1 d x = 2

\int_{6}^{8} \frac{6}{x ^{2}} d x = \frac{1}{4}

= 2 + \frac{1}{4}

Simplify

2 + \frac{1}{4} : \frac{9}{4}

= \frac{9}{4}

\int \frac{x ^{3} - x ^{2} + x - 1}{x ^{2} + 9} d x

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

x \to 2 lim (lo g_{4} (x - 2))

\frac{d y}{d x} + 3 x^{2} y = x^{2}

\frac{d y}{d x} = 10 x e^{5 y}

What is the integral from 6 to 8 of ((x^2+6)/(x^2)) ?
The integral from 6 to 8 of ((x^2+6)/(x^2)) is 9/4