de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((x+4)^2)/(x^2)

Lösung

\int \frac{( x + 4 ) ^{2}}{x ^{2}} d x

Lösung

x + 8 ln ∣ x ∣ - \frac{16}{x} + C

Schritte zur Lösung

\int \frac{( x + 4 ) ^{2}}{x ^{2}} d x

Multipliziere aus

\frac{( x + 4 ) ^{2}}{x ^{2}} : 1 + \frac{8}{x} + \frac{16}{x ^{2}}

= \int 1 + \frac{8}{x} + \frac{16}{x ^{2}} 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 1 d x + \int \frac{8}{x} d x + \int \frac{16}{x ^{2}} d x

\int 1 d x = x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int \frac{16}{x ^{2}} d x = - \frac{16}{x}

= x + 8 ln ∣ x ∣ - \frac{16}{x}

Füge eine Konstante zur Lösung hinzu

= x + 8 ln ∣ x ∣ - \frac{16}{x} + C

Graph

Beliebte Beispiele

integral of sqrt(x^2+4x+1)

\int x^{2} + 4 x + 1 d x

integral of x^2(x^3+2)^6

\int x^{2} (x^{3} + 2)^{6} d x

integral of (x^4+x^2+1)/(x^2)

\int \frac{x ^{4} + x ^{2} + 1}{x ^{2}} d x

integral of 1/(r+1)

\int \frac{1}{r + 1} d r

integral of e^{2x}cos(pi)x

\int e^{2 x} cos (π) x d x