What is the integral from 1 to infinity of x*4/(x^5) ?

The integral from 1 to infinity of x*4/(x^5) is 4/3

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integral from 1 to infinity of x*4/(x^5)

\int_{1}^{\infty} x \cdot \frac{4}{x ^{5}} d x

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

\int_{1}^{\infty} x \frac{4}{x ^{5}} d x

Compute the indefinite integral:

\int x \frac{4}{x ^{5}} d x = - \frac{4}{3 x ^{3}} + C

Compute the boundaries:

\int_{1}^{\infty} x \frac{4}{x ^{5}} d x = 0 - (- \frac{4}{3})

= 0 - (- \frac{4}{3})

Simplify

= \frac{4}{3}

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What is the integral from 1 to infinity of x*4/(x^5) ?
The integral from 1 to infinity of x*4/(x^5) is 4/3