What is the integral of 8x^{-5}y^7-10x^{-6}y^8 ?

The integral of 8x^{-5}y^7-10x^{-6}y^8 is (2y^8)/(x^5)-(2y^7)/(x^4)+C

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integral of 8x^{-5}y^7-10x^{-6}y^8

\int 8 x^{- 5} y^{7} - 10 x^{- 6} y^{8} d x

\frac{2 y ^{8}}{x ^{5}} - \frac{2 y ^{7}}{x ^{4}} + C

Solution steps

\int 8 x^{- 5} y^{7} - 10 x^{- 6} y^{8} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 10 y^{8} x^{- 6} d x + \int 8 y^{7} x^{- 5} d x

\int 10 y^{8} x^{- 6} d x = - \frac{2 y ^{8}}{x ^{5}}

\int 8 y^{7} x^{- 5} d x = - \frac{2 y ^{7}}{x ^{4}}

= - (- \frac{2 y ^{8}}{x ^{5}}) - \frac{2 y ^{7}}{x ^{4}}

Simplify

= \frac{2 y ^{8}}{x ^{5}} - \frac{2 y ^{7}}{x ^{4}}

Add a constant to the solution

= \frac{2 y ^{8}}{x ^{5}} - \frac{2 y ^{7}}{x ^{4}} + C

y = ln (ln (5 x))

\frac{d}{d x} (\frac{15}{x})

x \to 4 - lim (x^{2} + \frac{2}{x + 4})

x \to \infty lim (3^{- x})

(1, - 1), (5, - 7)

What is the integral of 8x^{-5}y^7-10x^{-6}y^8 ?
The integral of 8x^{-5}y^7-10x^{-6}y^8 is (2y^8)/(x^5)-(2y^7)/(x^4)+C