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

解

\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

解答ステップ

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

総和規則を適用する:

\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})

定数を解答に追加する

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