integral ((1-x^2))/((e^2x))

Lösung

integral

\frac{( 1 - x ^{2} )}{( e ^{2} x )}

\frac{1}{e ^{2}} (ln ∣ x ∣ - \frac{x ^{2}}{2}) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

\frac{1 - x ^{2}}{x} : \frac{1}{x} - x

= \frac{1}{e ^{2}} \cdot \int \frac{1}{x} - 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

= \frac{1}{e ^{2}} (\int \frac{1}{x} d x - \int x d x)

\int \frac{1}{x} d x = ln ∣ x ∣

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

= \frac{1}{e ^{2}} (ln ∣ x ∣ - \frac{x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{e ^{2}} (ln ∣ x ∣ - \frac{x ^{2}}{2}) + C

in t e g r a l \frac{x ^{- 2}}{3}

in t e g r a l \frac{( x ^{2} - 2 )}{( x + 4 )}

in t e g r a l (\frac{1}{x}) sin (\frac{1}{x})

in t e g r a l \frac{- 2}{y}

in t e g r a l 8 x - x^{2}