de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (7x)/(x+3)

Lösung

\int \frac{7 x}{x + 3} d x

Lösung

7 (x + 3 - 3 ln ∣ x + 3 ∣) + C

Schritte zur Lösung

\int \frac{7 x}{x + 3} d x

Entferne die Konstante:

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

= 7 \cdot \int \frac{x}{x + 3} d x

Wende U-Substitution an

= 7 \cdot \int \frac{u - 3}{u} d u

Multipliziere aus

\frac{u - 3}{u} : 1 - \frac{3}{u}

= 7 \cdot \int 1 - \frac{3}{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 7 (\int 1 d u - \int \frac{3}{u} d u)

\int 1 d u = u

\int \frac{3}{u} d u = 3 ln ∣ u ∣

= 7 (u - 3 ln ∣ u ∣)

Setze in

u = x + 3

ein

= 7 (x + 3 - 3 ln ∣ x + 3 ∣)

Füge eine Konstante zur Lösung hinzu

= 7 (x + 3 - 3 ln ∣ x + 3 ∣) + C

Graph

Beliebte Beispiele

integral of x^2(x^3+1)^{100}

\int x^{2} (x^{3} + 1)^{100} d x

integral of (x^4-3x^{3/2}+(7/(sqrt(x)))+5)

\int (x^{4} - 3 x^{\frac{3}{2}} + (\frac{7}{x}) + 5) d x

integral of 1/(sqrt(16-6x-x^2))

\int \frac{1}{16 - 6 x - x ^{2}} d x

integral of x^{-7/8}

\int x^{- \frac{7}{8}} d x

integral of 1/((y^2+7)^{3/2)}

\int \frac{1}{( y ^{2} + 7 ) ^{\frac{3}{2}}} d y