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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{5}{2} x + \frac{15}{4} - \frac{17}{4} ln ∣ 2 x + 3 ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{5 x - 1}{2 x + 3} : \frac{5 x}{2 x + 3} - \frac{1}{2 x + 3}

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

\int \frac{5 x}{2 x + 3} d x = \frac{5}{4} (2 x + 3 - 3 ln ∣ 2 x + 3 ∣)

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

= \frac{5}{4} (2 x + 3 - 3 ln ∣ 2 x + 3 ∣) - \frac{1}{2} ln ∣ 2 x + 3 ∣

Vereinfache

\frac{5}{4} (2 x + 3 - 3 ln ∣ 2 x + 3 ∣) - \frac{1}{2} ln ∣ 2 x + 3 ∣ : \frac{5}{2} x + \frac{15}{4} - \frac{17}{4} ln ∣ 2 x + 3 ∣

= \frac{5}{2} x + \frac{15}{4} - \frac{17}{4} ln ∣ 2 x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{5}{2} x + \frac{15}{4} - \frac{17}{4} ln ∣ 2 x + 3 ∣ + C

Graph

Beliebte Beispiele

integral of 1/(csc^4(y/2))

\int \frac{1}{csc ^{4} ( \frac{y}{2} )} d y

integral of 4/(t-sqrt(t+7)+1)

\int \frac{4}{t - t + 7 + 1} d t

integral of sin(sqrt(5x+1))

\int sin (5 x + 1) d x

integral of (4x+2)/(sqrt(4x-1))

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

integral of csc^4(b)x

\int csc^{4} (b) x d x