What is the integral from 1 to infinity of 1/(x^8) ?

The integral from 1 to infinity of 1/(x^8) is 1/7

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integral from 1 to infinity of 1/(x^8)

\int_{1}^{\infty} \frac{1}{x ^{8}} d x

\frac{1}{7}

Decimal Notation

0.14285 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{x ^{8}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{8}} d x = - \frac{1}{7 x ^{7}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x ^{8}} d x = 0 - (- \frac{1}{7})

= 0 - (- \frac{1}{7})

Simplify

= \frac{1}{7}

\frac{\partial}{\partial x} (4 x y - 3 x^{2})

y^{^{'}} = 2 x, y (1) = 7

x y^{^{'}} = x^{2} sin (x) + y

f (x) = \frac{36 x}{x ^{2} + 36}

\int \frac{( 4 x ^{2} )}{( x - 2 ) ( x ^{2} + 4 )} d x

What is the integral from 1 to infinity of 1/(x^8) ?
The integral from 1 to infinity of 1/(x^8) is 1/7