integral of ((tan(u))/4-4/7 u^6-2/u)

解

\int (\frac{tan ( u )}{4} - \frac{4}{7} u^{6} - \frac{2}{u}) d u

- \frac{1}{4} ln ∣ cos (u) ∣ - \frac{4 u ^{7}}{49} - 2 ln ∣ u ∣ + C

解答ステップ

\int \frac{tan ( u )}{4} - \frac{4}{7} u^{6} - \frac{2}{u} d u

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{tan ( u )}{4} d u - \int \frac{4}{7} u^{6} d u - \int \frac{2}{u} d u

\int \frac{tan ( u )}{4} d u = - \frac{1}{4} ln ∣ cos (u) ∣

\int \frac{4}{7} u^{6} d u = \frac{4 u ^{7}}{49}

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= - \frac{1}{4} ln ∣ cos (u) ∣ - \frac{4 u ^{7}}{49} - 2 ln ∣ u ∣

定数を解答に追加する

= - \frac{1}{4} ln ∣ cos (u) ∣ - \frac{4 u ^{7}}{49} - 2 ln ∣ u ∣ + C