integral of (e^{x/n}-a^{x/n})

Lösung

\int (e^{\frac{x}{n}} - a^{\frac{x}{n}}) d x

- \frac{n a ^{\frac{x}{n}}}{ln ( a )} + n e^{\frac{x}{n}} + C

Schritte zur Lösung

\int e^{\frac{x}{n}} - a^{\frac{x}{n}} 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 a^{\frac{x}{n}} d x + \int e^{\frac{x}{n}} d x

\int a^{\frac{x}{n}} d x = \frac{n a ^{\frac{x}{n}}}{ln ( a )}

\int e^{\frac{x}{n}} d x = n e^{\frac{x}{n}}

= - \frac{n a ^{\frac{x}{n}}}{ln ( a )} + n e^{\frac{x}{n}}

Füge eine Konstante zur Lösung hinzu

= - \frac{n a ^{\frac{x}{n}}}{ln ( a )} + n e^{\frac{x}{n}} + C

\int sec^{2} (- 0.578 t) d t

\int x 1 + \frac{1}{4} x d x

\int t + sin (t) d t

\int - sin (x) e^{- x} d x

\int \frac{e ^{\frac{x}{2}}}{x} d x