integral of 0.2+25x-200x^2+675x^3-900x^4+400x^5

解

\int 0.2 + 25 x - 200 x^{2} + 675 x^{3} - 900 x^{4} + 400 x^{5} d x

0.2 x + 12.5 x^{2} - 66.66666 \dots x^{3} + 168.75 x^{4} - 180 x^{5} + 66.66666 \dots x^{6} + C

解答ステップ

\int 0.2 + 25 x - 200 x^{2} + 675 x^{3} - 900 x^{4} + 400 x^{5} 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 0.2 d x + \int 25 x d x - \int 200 x^{2} d x + \int 675 x^{3} d x - \int 900 x^{4} d x + \int 400 x^{5} d x

\int 0.2 d x = 0.2 x

\int 25 x d x = \frac{25 x ^{2}}{2}

\int 200 x^{2} d x = \frac{200 x ^{3}}{3}

\int 675 x^{3} d x = \frac{675 x ^{4}}{4}

\int 900 x^{4} d x = 180 x^{5}

\int 400 x^{5} d x = \frac{200 x ^{6}}{3}

= 0.2 x + \frac{25 x ^{2}}{2} - \frac{200 x ^{3}}{3} + \frac{675 x ^{4}}{4} - 180 x^{5} + \frac{200 x ^{6}}{3}

簡素化

= 0.2 x + 12.5 x^{2} - 66.66666 \dots x^{3} + 168.75 x^{4} - 180 x^{5} + 66.66666 \dots x^{6}

定数を解答に追加する

= 0.2 x + 12.5 x^{2} - 66.66666 \dots x^{3} + 168.75 x^{4} - 180 x^{5} + 66.66666 \dots x^{6} + C