integral of (10x^3+7/(x^2)-x)

解

\int (10 x^{3} + \frac{7}{x ^{2}} - x) d x

\frac{5 x ^{4}}{2} - \frac{7}{x} - \frac{x ^{2}}{2} + C

解答ステップ

\int 10 x^{3} + \frac{7}{x ^{2}} - x 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 10 x^{3} d x + \int \frac{7}{x ^{2}} d x - \int x d x

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

\int \frac{7}{x ^{2}} d x = - \frac{7}{x}

\int x d x = \frac{x ^{2}}{2}

= \frac{5 x ^{4}}{2} - \frac{7}{x} - \frac{x ^{2}}{2}

定数を解答に追加する

= \frac{5 x ^{4}}{2} - \frac{7}{x} - \frac{x ^{2}}{2} + C