integral of ((-4x-4x^5)/(x^2)+5e^{7x})

Lösung

\int (\frac{- 4 x - 4 x ^{5}}{x ^{2}} + 5 e^{7 x}) d x

- x^{4} - 4 ln ∣ x ∣ + \frac{5}{7} e^{7 x} + C

Schritte zur Lösung

\int \frac{- 4 x - 4 x ^{5}}{x ^{2}} + 5 e^{7 x} d x

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{- 4 x - 4 x ^{5}}{x ^{2}} d x + \int 5 e^{7 x} d x

\int \frac{- 4 x - 4 x ^{5}}{x ^{2}} d x = - x^{4} - 4 ln ∣ x ∣

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

= - x^{4} - 4 ln ∣ x ∣ + \frac{5}{7} e^{7 x}

Füge eine Konstante zur Lösung hinzu

= - x^{4} - 4 ln ∣ x ∣ + \frac{5}{7} e^{7 x} + C

\int x (1 + x^{2})^{3} d x

\int 5 x e^{- 2 x^{2}} d x

\int \frac{4 x ^{2}}{( x ^{2} - 9 ) ^{\frac{3}{2}}} d x

\int \frac{e ^{- x}}{e ^{- 2 x} + 1} d x

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