integral ((2x-3))/((x-2))

Lösung

integral

\frac{( 2 x - 3 )}{( x - 2 )}

2 x - 4 + ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{2 x - 3}{x - 2} : \frac{2 x}{x - 2} - \frac{3}{x - 2}

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

\int \frac{2 x}{x - 2} d x = 2 (x - 2 + 2 ln ∣ x - 2 ∣)

\int \frac{3}{x - 2} d x = 3 ln ∣ x - 2 ∣

= 2 (x - 2 + 2 ln ∣ x - 2 ∣) - 3 ln ∣ x - 2 ∣

Vereinfache

2 (x - 2 + 2 ln ∣ x - 2 ∣) - 3 ln ∣ x - 2 ∣ : 2 x - 4 + ln ∣ x - 2 ∣

= 2 x - 4 + ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= 2 x - 4 + ln ∣ x - 2 ∣ + C

in t e g r a l \frac{cos ( x )}{( 1 + sin ( x ) ) ^{3}}

in t e g r a l \frac{( x ^{4} + 3 )}{x}

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

in t e g r a l (x^{2} - 5 x) e^{x}

in t e g r a l \frac{( x + 3 )}{( x ^{2} + 3 )}