de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

\frac{2 x - 1}{4 x ^{2} - 1} : \frac{2 x}{4 x ^{2} - 1} - \frac{1}{4 x ^{2} - 1}

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

\int \frac{2 x}{4 x ^{2} - 1} d x = \frac{1}{4} ln 4 x^{2} - 1

\int \frac{1}{4 x ^{2} - 1} d x = - \frac{1}{4} (ln ∣ 2 x + 1 ∣ - ln ∣ 2 x - 1 ∣)

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

(\partial)/(\partial y)(5xy^2)

integral of (35)/(1-cos(5x))

derivative of x^5+x+1

derivative of (((0.06x^2+17x+340))/x)

laplacetransform 2e^{t/2}