integral of (e^a+1)/(e^a)

Lösung

\int \frac{e ^{a} + 1}{e ^{a}} d a

a - \frac{1}{e ^{a}} + C

Schritte zur Lösung

\int \frac{e ^{a} + 1}{e ^{a}} d a

Multipliziere aus

\frac{e ^{a} + 1}{e ^{a}} : 1 + \frac{1}{e ^{a}}

= \int 1 + \frac{1}{e ^{a}} d a

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d a + \int \frac{1}{e ^{a}} d a

\int 1 d a = a

\int \frac{1}{e ^{a}} d a = - \frac{1}{e ^{a}}

= a - \frac{1}{e ^{a}}

Füge eine Konstante zur Lösung hinzu

= a - \frac{1}{e ^{a}} + C

x \to - 8 lim (\frac{x ^{2} - 4}{8 - x})

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

x \to 0 lim (f (x) (x^{2}))

\frac{d x}{d t} = 1

t an g e n t y = x^{2} - x^{4}, (0, 1)