integral of (7x^4+4sqrt(x)+1/(x^3))

解

\int (7 x^{4} + 4 x + \frac{1}{x ^{3}}) d x

\frac{7 x ^{5}}{5} + \frac{8}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C

解答ステップ

\int 7 x^{4} + 4 x + \frac{1}{x ^{3}} 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^{4} d x + \int 4 x d x + \int \frac{1}{x ^{3}} d x

\int 7 x^{4} d x = \frac{7 x ^{5}}{5}

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

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

= \frac{7 x ^{5}}{5} + \frac{8}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}}

定数を解答に追加する

= \frac{7 x ^{5}}{5} + \frac{8}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C