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

Lösung

\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

Schritte zur Lösung

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

Wende die Summenregel an:

\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 ∣

Füge eine Konstante zur Lösung hinzu

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

x \to a lim (\frac{1}{2})

d er i v a t i v e f (x) = (5 x + 4)^{3}

\int_{0}^{5} \frac{1}{u ^{2} - 25} d u

t an g e n t y = 4 cos (x), (\frac{π}{3}, 2)

d er i v a t i v e - x^{- 2} e^{\frac{1}{x}}