What is the integral of y^{-4}+3/x ?

The integral of y^{-4}+3/x is 3ln|x|+x/(y^4)+C

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integral of y^{-4}+3/x

\int y^{- 4} + \frac{3}{x} d x

3 ln ∣ x ∣ + \frac{x}{y ^{4}} + C

Solution steps

\int y^{- 4} + \frac{3}{x} 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 \frac{3}{x} d x + \int y^{- 4} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ + \frac{x}{y ^{4}}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{x}{y ^{4}} + C

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What is the integral of y^{-4}+3/x ?
The integral of y^{-4}+3/x is 3ln|x|+x/(y^4)+C