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

The integral from 1 to 5 of (3x)/(x^3) is 12/5

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

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

\frac{12}{5}

Decimal Notation

2.4

Solution steps

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

Take the constant out:

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

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

Cancel the common factor:

x

= 3 \cdot \int_{1}^{5} \frac{1}{x ^{2}} d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{4}{5}

= 3 \cdot \frac{4}{5}

Simplify

= \frac{12}{5}

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What is the integral from 1 to 5 of (3x)/(x^3) ?
The integral from 1 to 5 of (3x)/(x^3) is 12/5