integral of (162)/(x^3)+2sqrt(x)

解

\int \frac{162}{x ^{3}} + 2 x d x

- \frac{81}{x ^{2}} + \frac{4}{3} x^{\frac{3}{2}} + C

解答ステップ

\int \frac{162}{x ^{3}} + 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 \frac{162}{x ^{3}} d x + \int 2 x d x

\int \frac{162}{x ^{3}} d x = - \frac{81}{x ^{2}}

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

= - \frac{81}{x ^{2}} + \frac{4}{3} x^{\frac{3}{2}}

定数を解答に追加する

= - \frac{81}{x ^{2}} + \frac{4}{3} x^{\frac{3}{2}} + C