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Beliebt Rechnen >

integral of (2x)/(5x+3)

Lösung

\int \frac{2 x}{5 x + 3} d x

Lösung

2 (\frac{1}{5} x - \frac{3}{25} ln ∣ 5 x + 3 ∣) + C

Schritte zur Lösung

\int \frac{2 x}{5 x + 3} d x

Entferne die Konstante:

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

= 2 \cdot \int \frac{x}{5 x + 3} d x

Lange Division

\frac{x}{5 x + 3} : \frac{1}{5} - \frac{3}{5 ( 5 x + 3 )}

= 2 \cdot \int \frac{1}{5} - \frac{3}{5 ( 5 x + 3 )} 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

= 2 (\int \frac{1}{5} d x - \int \frac{3}{5 ( 5 x + 3 )} d x)

\int \frac{1}{5} d x = \frac{1}{5} x

\int \frac{3}{5 ( 5 x + 3 )} d x = \frac{3}{25} ln ∣ 5 x + 3 ∣

= 2 (\frac{1}{5} x - \frac{3}{25} ln ∣ 5 x + 3 ∣)

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{1}{5} x - \frac{3}{25} ln ∣ 5 x + 3 ∣) + C

Graph

Beliebte Beispiele

integral of e^{ax}sin(x)

\int e^{a x} sin (x) d x

integral of x/(\sqrt[4]{x+5)}

\int \frac{x}{4 x + 5} d x

integral of 1/(3x^2+5x+1)

\int \frac{1}{3 x ^{2} + 5 x + 1} d x

integral of 1/(sqrt(e^{2x)-25)}

\int \frac{1}{e ^{2 x} - 25} d x

integral of (-1)/(x(ln(x))^3)

\int \frac{- 1}{x ( ln ( x ) ) ^{3}} d x