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

The integral from-3 to-1 of 5/(x^4) is 130/81

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integral from-3 to-1 of 5/(x^4)

\int_{- 3}^{- 1} \frac{5}{x ^{4}} d x

\frac{130}{81}

Decimal

1.60493 \dots

Solution steps

\int_{- 3}^{- 1} \frac{5}{x ^{4}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{- 3}^{- 1} \frac{1}{x ^{4}} d x

Apply the Power Rule

: [- \frac{1}{3 x ^{3}}]_{- 3}^{- 1}

= 5 [- \frac{1}{3 x ^{3}}]_{- 3}^{- 1}

Compute the boundaries:

\frac{26}{81}

= 5 \cdot \frac{26}{81}

Simplify

= \frac{130}{81}

f (x) = \frac{27}{5 x ^{2}} - \frac{3}{2}, at x = 1

\int_{1}^{5} \frac{x ^{2} + 5}{6 x - x ^{2}} d x

\frac{d y}{d x} = \frac{( x y + x )}{y}

y^{^{''}} + 2 π y^{^{'}} + π^{2} y = 0

\frac{d y}{d x} = \frac{x ^{2} - 2}{3 y}

What is the integral from-3 to-1 of 5/(x^4) ?
The integral from-3 to-1 of 5/(x^4) is 130/81