de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (3x^2+1)/(x-4)

Lösung

\int \frac{3 x ^{2} + 1}{x - 4} d x

Lösung

\frac{3}{2} (x - 4)^{2} + 24 x - 96 + 49 ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{3 x ^{2} + 1}{x - 4} d x

Multipliziere aus

\frac{3 x ^{2} + 1}{x - 4} : \frac{3 x ^{2}}{x - 4} + \frac{1}{x - 4}

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

\int \frac{3 x ^{2}}{x - 4} d x = 3 (\frac{( x - 4 ) ^{2}}{2} + 8 (x - 4) + 16 ln ∣ x - 4 ∣)

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

= 3 (\frac{( x - 4 ) ^{2}}{2} + 8 (x - 4) + 16 ln ∣ x - 4 ∣) + ln ∣ x - 4 ∣

Vereinfache

3 (\frac{( x - 4 ) ^{2}}{2} + 8 (x - 4) + 16 ln ∣ x - 4 ∣) + ln ∣ x - 4 ∣ : \frac{3}{2} (x - 4)^{2} + 24 x - 96 + 49 ln ∣ x - 4 ∣

= \frac{3}{2} (x - 4)^{2} + 24 x - 96 + 49 ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} (x - 4)^{2} + 24 x - 96 + 49 ln ∣ x - 4 ∣ + C

Graph

Beliebte Beispiele

integral of (sqrt(y))/(sqrt(y^3)+4)

\int \frac{y}{y ^{3} + 4} d y

integral of ((cos(3t)+3))/(sin(3t))

\int \frac{( cos ( 3 t ) + 3 )}{sin ( 3 t )} d t

integral of (10^{3x}-2^x)

\int (1 0^{3 x} - 2^{x}) d x

integral of 20x^4(4x^5-1)^4

\int 20 x^{4} (4 x^{5} - 1)^{4} d x

integral of 3.1x+2.7

\int 3.1 x + 2.7 d x