integral ((1+x)^2)/(x^2)

Lösung

integral

\frac{( 1 + x ) ^{2}}{x ^{2}}

- \frac{1}{x} + 2 ln ∣ x ∣ + x + C

Schritte zur Lösung

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

Multipliziere aus

\frac{( 1 + x ) ^{2}}{x ^{2}} : \frac{1}{x ^{2}} + \frac{2}{x} + 1

= \int \frac{1}{x ^{2}} + \frac{2}{x} + 1 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{1}{x ^{2}} d x + \int \frac{2}{x} d x + \int 1 d x

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 1 d x = x

= - \frac{1}{x} + 2 ln ∣ x ∣ + x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{x} + 2 ln ∣ x ∣ + x + C

in t e g r a l \frac{( 1 - x ^{2} )}{( e ^{2} x )}

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}