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

The integral from 1 to 4 of 5/(x^3) is 75/32

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

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

\frac{75}{32}

Decimal

2.34375

Solution steps

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

Apply the Power Rule

= 5 [- \frac{1}{2 x ^{2}}]_{1}^{4}

Compute the boundaries:

\frac{15}{32}

= 5 \cdot \frac{15}{32}

Simplify

= \frac{75}{32}

What is the integral from 1 to 4 of 5/(x^3) ?
The integral from 1 to 4 of 5/(x^3) is 75/32