What is the integral from 0 to 1 of (45)/(x^5) ?

The integral from 0 to 1 of (45)/(x^5) is diverges

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integral from 0 to 1 of (45)/(x^5)

\int_{0}^{1} \frac{45}{x ^{5}} d x

diverges

Solution steps

\int_{0}^{1} \frac{45}{x ^{5}} d x

Take the constant out:

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

= 45 \cdot \int_{0}^{1} \frac{1}{x ^{5}} d x

Apply the Power Rule

: [- \frac{1}{4 x ^{4}}]_{0}^{1}

= 45 [- \frac{1}{4 x ^{4}}]_{0}^{1}

Compute the boundaries:

diverges

= diverges

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f (x) = \frac{- x ^{2} - 1}{( x ^{2} + 1 ) ^{2}}

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What is the integral from 0 to 1 of (45)/(x^5) ?
The integral from 0 to 1 of (45)/(x^5) is diverges