What is the integral from 0 to 1 of 21 1/(x^p) ?

The integral from 0 to 1 of 21 1/(x^p) is (21)/(-p+1)

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integral from 0 to 1 of 21 1/(x^p)

\int_{0}^{1} 21 \frac{1}{x ^{p}} d x

\frac{21}{- p + 1}

Solution steps

\int_{0}^{1} 21 \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

= 21 \cdot \int_{0}^{1} \frac{1}{x ^{p}} d x

Apply the Power Rule

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

= 21 [\frac{x ^{- p + 1}}{- p + 1}]_{0}^{1}

Compute the boundaries:

\frac{1}{- p + 1}

= 21 \cdot \frac{1}{- p + 1}

Simplify

= \frac{21}{- p + 1}

\int x e^{x^{2}} cos (x^{2}) d x

\frac{d}{d x} (\frac{1 - 2 x}{3 x ^{2}})

x \to 1 lim (\frac{2}{x ^{3} - x})

\frac{d}{d x} ((\frac{x + 5}{x ^{2} + 2})^{2})

\frac{d ^{2}}{d x ^{2}} (e^{\frac{6}{x}})

What is the integral from 0 to 1 of 21 1/(x^p) ?
The integral from 0 to 1 of 21 1/(x^p) is (21)/(-p+1)