integral of (7x^3+5x^2+9/(x^2)+2/(a^2))

解

\int (7 x^{3} + 5 x^{2} + \frac{9}{x ^{2}} + \frac{2}{a ^{2}}) d x

\frac{7 x ^{4}}{4} + \frac{5 x ^{3}}{3} - \frac{9}{x} + \frac{2}{a ^{2}} x + C

解答ステップ

\int 7 x^{3} + 5 x^{2} + \frac{9}{x ^{2}} + \frac{2}{a ^{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 7 x^{3} d x + \int 5 x^{2} d x + \int \frac{9}{x ^{2}} d x + \int \frac{2}{a ^{2}} d x

\int 7 x^{3} d x = \frac{7 x ^{4}}{4}

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

\int \frac{9}{x ^{2}} d x = - \frac{9}{x}

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

= \frac{7 x ^{4}}{4} + \frac{5 x ^{3}}{3} - \frac{9}{x} + \frac{2}{a ^{2}} x

定数を解答に追加する

= \frac{7 x ^{4}}{4} + \frac{5 x ^{3}}{3} - \frac{9}{x} + \frac{2}{a ^{2}} x + C