integral ((1+x)^3)/(x^2)

Lösung

integral

\frac{( 1 + x ) ^{3}}{x ^{2}}

- \frac{1}{x} + 3 ln ∣ x ∣ + 3 x + \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int \frac{( 1 + x ) ^{3}}{x ^{2}} d x

Multipliziere aus

\frac{( 1 + x ) ^{3}}{x ^{2}} : \frac{1}{x ^{2}} + \frac{3}{x} + 3 + x

= \int \frac{1}{x ^{2}} + \frac{3}{x} + 3 + 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

= \int \frac{1}{x ^{2}} d x + \int \frac{3}{x} d x + \int 3 d x + \int x d x

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 3 d x = 3 x

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

= - \frac{1}{x} + 3 ln ∣ x ∣ + 3 x + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{x} + 3 ln ∣ x ∣ + 3 x + \frac{x ^{2}}{2} + C

in t e g r a l x \cdot 3^{x}

in t e g r a l 1 + cos^{2} (x)

in t e g r a l x^{\frac{1}{3}}

in t e g r a l ((9^{9})^{9})^{x}

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