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Popular >

integral of 5x^{-9}

Solution

\int 5 x^{- 9} d x

Solution

- \frac{5}{8 x ^{8}} + C

Solution steps

\int 5 x^{- 9} d x

Take the constant out:

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

= 5 \cdot \int x^{- 9} d x

Apply the Power Rule

: - \frac{1}{8 x ^{8}}

= 5 (- \frac{1}{8 x ^{8}})

Simplify

5 (- \frac{1}{8 x ^{8}}) : - \frac{5}{8 x ^{8}}

= - \frac{5}{8 x ^{8}}

Add a constant to the solution

= - \frac{5}{8 x ^{8}} + C

Popular Examples

integral of 9/(cos(θ)-1)

\int \frac{9}{cos ( θ ) - 1} d θ

integral of (7x-5)/(9x^2+4)

\int \frac{7 x - 5}{9 x ^{2} + 4} d x

integral of x/((x+1)(x^2+x+1))

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

integral of (x^5-x^{6/5}-9x+2)/(x^{1/3)}

\int \frac{x ^{5} - x ^{\frac{6}{5}} - 9 x + 2}{x ^{\frac{1}{3}}} d x

integral of w/(sqrt(1-w^4))

\int \frac{w}{1 - w ^{4}} d w

Frequently Asked Questions (FAQ)

What is the integral of 5x^{-9} ?
The integral of 5x^{-9} is -5/(8x^8)+C