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Popular >

integral of 1/(x^a)

Solution

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

Solution

\frac{x ^{- a + 1}}{- a + 1} + C

Solution steps

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

Apply the Power Rule

: \frac{x ^{- a + 1}}{- a + 1}

= \frac{x ^{- a + 1}}{- a + 1}

Add a constant to the solution

= \frac{x ^{- a + 1}}{- a + 1} + C

Popular Examples

limit as x approaches-1+of x/(x+1)

x \to - 1 + lim (\frac{x}{x + 1})

(\partial)/(\partial t)(sqrt(3t))

\frac{\partial}{\partial t} (3 t)

(dy)/(dx)=(x+y-2)/(2x+2y+3)

\frac{d y}{d x} = \frac{x + y - 2}{2 x + 2 y + 3}

integral of 1/(x^2-25)

\int \frac{1}{x ^{2} - 25} d x

(\partial)/(\partial x)(cos(x^8+y^8))

\frac{\partial}{\partial x} (cos (x^{8} + y^{8}))

Frequently Asked Questions (FAQ)

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