integral of x^4-8x^3+26x^2-40x+25

解

\int x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25 d x

\frac{x ^{5}}{5} - 2 x^{4} + \frac{26 x ^{3}}{3} - 20 x^{2} + 25 x + C

解答ステップ

\int x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25 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^{4} d x - \int 8 x^{3} d x + \int 26 x^{2} d x - \int 40 x d x + \int 25 d x

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

\int 8 x^{3} d x = 2 x^{4}

\int 26 x^{2} d x = \frac{26 x ^{3}}{3}

\int 40 x d x = 20 x^{2}

\int 25 d x = 25 x

= \frac{x ^{5}}{5} - 2 x^{4} + \frac{26 x ^{3}}{3} - 20 x^{2} + 25 x

定数を解答に追加する

= \frac{x ^{5}}{5} - 2 x^{4} + \frac{26 x ^{3}}{3} - 20 x^{2} + 25 x + C