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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{2}}{2} + x + \frac{1}{4} ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int x + 1 + \frac{1}{4 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 x d x + \int 1 d x + \int \frac{1}{4 x} d x

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

\int 1 d x = x

\int \frac{1}{4 x} d x = \frac{1}{4} ln ∣ x ∣

= \frac{x ^{2}}{2} + x + \frac{1}{4} ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + x + \frac{1}{4} ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (x+8)/(x^2+3x)

\int \frac{x + 8}{x ^{2} + 3 x} d x

integral of ((sqrt(x)+x))/(sqrt(x))

\int \frac{( x + x )}{x} d x

integral of 1/(4+9x)

\int \frac{1}{4 + 9 x} d x

integral of x^2sqrt(3x^3+1)

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

integral of (sec(m)x+tan(m)x)^2

\int (sec (m) x + tan (m) x)^{2} d x