What is the integral of a/(x^{a+1)} ?

The integral of a/(x^{a+1)} is -x^{-a}+C

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integral of a/(x^{a+1)}

\int \frac{a}{x ^{a + 1}} d x

- x^{- a} + C

Solution steps

\int \frac{a}{x ^{a + 1}} d x

Take the constant out:

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

= a \cdot \int \frac{1}{x ^{a + 1}} d x

Apply the Power Rule

: - \frac{x ^{- a}}{a}

= a (- \frac{x ^{- a}}{a})

Simplify

a (- \frac{x ^{- a}}{a}) : - x^{- a}

= - x^{- a}

Add a constant to the solution

= - x^{- a} + C

\frac{\partial}{\partial x} (x^{2} + y^{2} - 2)

\int \frac{1}{x ^{2} x ^{2} - 4} d x

\int \frac{2}{x ( x ^{4} + 25 ) ^{\frac{1}{2}}} d x

h \to 2 lim (\frac{h ^{3} + 8}{h + 2})