What is the integral from 1 to 1000 of 5/(x^3) ?

The integral from 1 to 1000 of 5/(x^3) is 999999/400000

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integral from 1 to 1000 of 5/(x^3)

\int_{1}^{1000} \frac{5}{x ^{3}} d x

\frac{999999}{400000}

Decimal Notation

2.4999975

Solution steps

\int_{1}^{1000} \frac{5}{x ^{3}} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{1000} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{1}^{1000}

= 5 [- \frac{1}{2 x ^{2}}]_{1}^{1000}

Compute the boundaries:

\frac{999999}{2000000}

= 5 \cdot \frac{999999}{2000000}

Simplify

= \frac{999999}{400000}

f (x) = 5 x + 75, at x = 5

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

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

\frac{d}{d x} (3 x^{4} - 3 x^{3} - 2)

x \to 1 - lim (3 x)

What is the integral from 1 to 1000 of 5/(x^3) ?
The integral from 1 to 1000 of 5/(x^3) is 999999/400000