What is the integral from 0 to 1 of 30 1/(x^p) ?

The integral from 0 to 1 of 30 1/(x^p) is (30)/(-p+1)

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integral from 0 to 1 of 30 1/(x^p)

\int_{0}^{1} 30 \frac{1}{x ^{p}} d x

\frac{30}{- p + 1}

Solution steps

\int_{0}^{1} 30 \cdot \frac{1}{x ^{p}} d x

Take the constant out:

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

= 30 \cdot \int_{0}^{1} \frac{1}{x ^{p}} d x

Apply the Power Rule

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

= 30 [\frac{x ^{- p + 1}}{- p + 1}]_{0}^{1}

Compute the boundaries:

\frac{1}{- p + 1}

= 30 \cdot \frac{1}{- p + 1}

Simplify

= \frac{30}{- p + 1}

\frac{4 x + x ^{2}}{( 2 + x ) ^{2}}

\int \frac{u}{1 + 2 u} d u

f (x) = 2 x^{2} - 12 x + 8

\frac{d}{d x} ((x^{2} + y^{2})^{3})

What is the integral from 0 to 1 of 30 1/(x^p) ?
The integral from 0 to 1 of 30 1/(x^p) is (30)/(-p+1)