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

The integral from 1 to infinity of 2/(x^4) is 2/3

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

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

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

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

Compute the indefinite integral:

\int \frac{2}{x ^{4}} d x = - \frac{2}{3 x ^{3}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{2}{x ^{4}} d x = 0 - (- \frac{2}{3})

= 0 - (- \frac{2}{3})

Simplify

= \frac{2}{3}

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