What is the integral of 1/((pi*x)^{10)} ?

The integral of 1/((pi*x)^{10)} is -1/(9pi^{10)x^9}+C

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integral of 1/((pi*x)^{10)}

\int \frac{1}{( π \cdot x ) ^{10}} d x

- \frac{1}{9 π ^{10} x ^{9}} + C

Solution steps

\int \frac{1}{( π x ) ^{10}} d x

(π x)^{10} = π^{10} x^{10}

= \int \frac{1}{π ^{10} x ^{10}} d x

Take the constant out:

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

= \frac{1}{π ^{10}} \cdot \int \frac{1}{x ^{10}} d x

Apply the Power Rule

: - \frac{1}{9 x ^{9}}

= \frac{1}{π ^{10}} (- \frac{1}{9 x ^{9}})

Simplify

\frac{1}{π ^{10}} (- \frac{1}{9 x ^{9}}) : - \frac{1}{9 π ^{10} x ^{9}}

= - \frac{1}{9 π ^{10} x ^{9}}

Add a constant to the solution

= - \frac{1}{9 π ^{10} x ^{9}} + C

\frac{d}{d x} (4 + x x)

\frac{x ^{2}}{1 - x ^{2}}

\frac{\partial}{\partial x} (x^{3} y + x cos (y))

\frac{d y}{d x} = \frac{1}{2} y^{3}

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{8}))

What is the integral of 1/((pi*x)^{10)} ?
The integral of 1/((pi*x)^{10)} is -1/(9pi^{10)x^9}+C