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人気のある微分積分 >

integral of (5x^4+3x^3-2)

解

\int (5 x^{4} + 3 x^{3} - 2) d x

解

x^{5} + \frac{3 x ^{4}}{4} - 2 x + C

解答ステップ

\int 5 x^{4} + 3 x^{3} - 2 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 5 x^{4} d x + \int 3 x^{3} d x - \int 2 d x

\int 5 x^{4} d x = x^{5}

\int 3 x^{3} d x = \frac{3 x ^{4}}{4}

\int 2 d x = 2 x

= x^{5} + \frac{3 x ^{4}}{4} - 2 x

定数を解答に追加する

= x^{5} + \frac{3 x ^{4}}{4} - 2 x + C

グラフ

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