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

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

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

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

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

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

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{1}^{3}

= 3 [- \frac{1}{2 x ^{2}}]_{1}^{3}

Compute the boundaries:

\frac{4}{9}

= 3 \cdot \frac{4}{9}

Simplify

= \frac{4}{3}

\int_{1}^{2} x (x^{2} - 1)^{7} d x

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

\int_{0}^{1} t cos (π t) d t

\int_{0}^{2} y^{2} y^{3} + 1 d y

\int_{4}^{7} 5 d x

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