What is the integral from 1 to infinity of x^{-7/4} ?

The integral from 1 to infinity of x^{-7/4} is 4/3

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integral from 1 to infinity of x^{-7/4}

\int_{1}^{\infty} x^{- \frac{7}{4}} d x

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

\int_{1}^{\infty} x^{- \frac{7}{4}} d x

Compute the indefinite integral:

\int x^{- \frac{7}{4}} d x = - \frac{4}{3 x ^{\frac{3}{4}}} + C

Compute the boundaries:

\int_{1}^{\infty} x^{- \frac{7}{4}} d x = 0 - (- \frac{4}{3})

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

Simplify

= \frac{4}{3}

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

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

x \to 3 lim (5 x^{3} - 3 x^{2} + x - 6)

\int e^{r t} d t

\int 2 x e^{x^{2} + y^{2}} d x

What is the integral from 1 to infinity of x^{-7/4} ?
The integral from 1 to infinity of x^{-7/4} is 4/3