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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

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

= \frac{1}{2} \cdot \int x + \frac{1}{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

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (4x^4)/(sqrt(5-12x^5))

\int \frac{4 x ^{4}}{5 - 12 x ^{5}} d x

integral of sin(4x)sqrt(cos(4x)+1)

\int sin (4 x) cos (4 x) + 1 d x

integral of x^2e^{(x^3)/3}

\int x^{2} e^{\frac{x ^{3}}{3}} d x

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

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

integral of 2/(7x^2+2x+1)

\int \frac{2}{7 x ^{2} + 2 x + 1} d x