de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/((x+5)^2(x-4))

Lösung

\int \frac{1}{( x + 5 ) ^{2} ( x - 4 )} d x

Lösung

- \frac{1}{81} ln ∣ x + 5 ∣ + \frac{1}{9 ( x + 5 )} + \frac{1}{81} ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x + 5 ) ^{2} ( x - 4 )} d x

Ermittle den Partialbruch von

\frac{1}{( x + 5 ) ^{2} ( x - 4 )} : - \frac{1}{81 ( x + 5 )} - \frac{1}{9 ( x + 5 ) ^{2}} + \frac{1}{81 ( x - 4 )}

= \int - \frac{1}{81 ( x + 5 )} - \frac{1}{9 ( x + 5 ) ^{2}} + \frac{1}{81 ( x - 4 )} 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

= - \int \frac{1}{81 ( x + 5 )} d x - \int \frac{1}{9 ( x + 5 ) ^{2}} d x + \int \frac{1}{81 ( x - 4 )} d x

\int \frac{1}{81 ( x + 5 )} d x = \frac{1}{81} ln ∣ x + 5 ∣

\int \frac{1}{9 ( x + 5 ) ^{2}} d x = - \frac{1}{9 ( x + 5 )}

\int \frac{1}{81 ( x - 4 )} d x = \frac{1}{81} ln ∣ x - 4 ∣

= - \frac{1}{81} ln ∣ x + 5 ∣ - (- \frac{1}{9 ( x + 5 )}) + \frac{1}{81} ln ∣ x - 4 ∣

Vereinfache

= - \frac{1}{81} ln ∣ x + 5 ∣ + \frac{1}{9 ( x + 5 )} + \frac{1}{81} ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{81} ln ∣ x + 5 ∣ + \frac{1}{9 ( x + 5 )} + \frac{1}{81} ln ∣ x - 4 ∣ + C

Graph

Beliebte Beispiele

d er i v a t i v e - 3 t

derivative of 6sin(sin(x))

\frac{d}{d x} (6 sin (sin (x)))

integral of sin^3(xco)s^5x

\int sin^{3} (x co) s^{5} x d x

derivative f(x)=tan(2x)*sin(2x)

d er i v a t i v e f (x) = tan (2 x) \cdot sin (2 x)

integral from-3 to 3 of (18-2x^2)

\int_{- 3}^{3} (18 - 2 x^{2}) d x