integral of 1/(x^4)-1/(\sqrt[4]{x)}-4

解

\int \frac{1}{x ^{4}} - \frac{1}{4 x} - 4 d x

- \frac{1}{3 x ^{3}} - \frac{4}{3} x^{\frac{3}{4}} - 4 x + C

解答ステップ

\int \frac{1}{x ^{4}} - \frac{1}{4 x} - 4 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{1}{x ^{4}} d x - \int \frac{1}{4 x} d x - \int 4 d x

\int \frac{1}{x ^{4}} d x = - \frac{1}{3 x ^{3}}

\int \frac{1}{4 x} d x = \frac{4}{3} x^{\frac{3}{4}}

\int 4 d x = 4 x

= - \frac{1}{3 x ^{3}} - \frac{4}{3} x^{\frac{3}{4}} - 4 x

定数を解答に追加する

= - \frac{1}{3 x ^{3}} - \frac{4}{3} x^{\frac{3}{4}} - 4 x + C