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

The integral of (-8x^7y^{-5}+6x^6y^{-4}) is -(2x^6)/(y^3)+(2x^7)/(y^4)+C

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integral of (-8x^7y^{-5}+6x^6y^{-4})

\int (- 8 x^{7} y^{- 5} + 6 x^{6} y^{- 4}) d y

- \frac{2 x ^{6}}{y ^{3}} + \frac{2 x ^{7}}{y ^{4}} + C

Solution steps

\int - 8 x^{7} y^{- 5} + 6 x^{6} y^{- 4} d y

Apply the Sum Rule:

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

= \int 6 x^{6} y^{- 4} d y - \int 8 x^{7} y^{- 5} d y

\int 6 x^{6} y^{- 4} d y = - \frac{2 x ^{6}}{y ^{3}}

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

= - \frac{2 x ^{6}}{y ^{3}} - (- \frac{2 x ^{7}}{y ^{4}})

Simplify

= - \frac{2 x ^{6}}{y ^{3}} + \frac{2 x ^{7}}{y ^{4}}

Add a constant to the solution

= - \frac{2 x ^{6}}{y ^{3}} + \frac{2 x ^{7}}{y ^{4}} + C

\int_{1}^{t} \frac{31}{x ^{3}} d x

x \to 0 lim (\frac{ln ^{2} ( x )}{x})

f (x) = ln^{3} (3 x - 5)

\int sec^{2} (t) + t (t^{2} + 1)^{3} + t^{2} ln (t) d t

\frac{d}{d x} (e^{s i n (3 x)})

What is the integral of (-8x^7y^{-5}+6x^6y^{-4}) ?
The integral of (-8x^7y^{-5}+6x^6y^{-4}) is -(2x^6)/(y^3)+(2x^7)/(y^4)+C