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

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

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Compute the indefinite integral:

\int \frac{1}{x ^{4}} d x = - \frac{1}{3 x ^{3}} + C

Compute the boundaries:

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

= 0 - (- \frac{1}{3})

Simplify

= \frac{1}{3}

\int e^{(x + 1)^{2}} (x + 1) d x

f (x) = \frac{1}{x} - 2, (- 1, - 3)

g (x) = x^{3} \cdot e^{x}

\int_{0}^{\frac{π}{6}} (3 sec^{2} (x)) d x

\int 3 cos (t) d t

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