What is the integral of x^3os(x^4+2)+x^{-1} ?

The integral of x^3os(x^4+2)+x^{-1} is ln|x|+os(1/4 x^4(2+x^4)-(x^8)/8)+C

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integral of x^3os(x^4+2)+x^{-1}

\int x^{3} os (x^{4} + 2) + x^{- 1}

ln ∣ x ∣ + os (\frac{1}{4} x^{4} (2 + x^{4}) - \frac{x ^{8}}{8}) + C

Solution steps

\int x^{3} os (x^{4} + 2) + x^{- 1} 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 x^{- 1} d x + \int (2 + x^{4}) os x^{3} d x

\int x^{- 1} d x = ln ∣ x ∣

\int (2 + x^{4}) os x^{3} d x = os (\frac{1}{4} x^{4} (2 + x^{4}) - \frac{x ^{8}}{8})

= ln ∣ x ∣ + os (\frac{1}{4} x^{4} (2 + x^{4}) - \frac{x ^{8}}{8})

Add a constant to the solution

= ln ∣ x ∣ + os (\frac{1}{4} x^{4} (2 + x^{4}) - \frac{x ^{8}}{8}) + C

What is the integral of x^3os(x^4+2)+x^{-1} ?
The integral of x^3os(x^4+2)+x^{-1} is ln|x|+os(1/4 x^4(2+x^4)-(x^8)/8)+C