What is the integral from 0 to 1 of 2/(x^3) ?

The integral from 0 to 1 of 2/(x^3) is diverges

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integral from 0 to 1 of 2/(x^3)

\int_{0}^{1} \frac{2}{x ^{3}} d x

diverges

Solution steps

\int_{0}^{1} \frac{2}{x ^{3}} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{1} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{0}^{1}

= 2 [- \frac{1}{2 x ^{2}}]_{0}^{1}

Compute the boundaries:

diverges

= diverges

\int_{0}^{1} - \frac{( x - 1 ) ^{3}}{3} d x

\int_{0}^{1} 2 π (2 - x) (x - x^{2}) d x

\int_{- 4}^{0} (- x^{2} - 4 x) d x

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

\int_{x}^{- 1} t^{2} + 1 d t

What is the integral from 0 to 1 of 2/(x^3) ?
The integral from 0 to 1 of 2/(x^3) is diverges