de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (13)/(x(x^2+25))

Lösung

\int \frac{13}{x ( x ^{2} + 25 )} d x

Lösung

13 (\frac{1}{25} ln ∣ x ∣ - \frac{1}{50} ln x^{2} + 25) + C

Schritte zur Lösung

\int \frac{13}{x ( x ^{2} + 25 )} d x

Entferne die Konstante:

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

= 13 \cdot \int \frac{1}{x ( x ^{2} + 25 )} d x

Ermittle den Partialbruch von

\frac{1}{x ( x ^{2} + 25 )} : \frac{1}{25 x} - \frac{x}{25 ( x ^{2} + 25 )}

= 13 \cdot \int \frac{1}{25 x} - \frac{x}{25 ( x ^{2} + 25 )} 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

= 13 (\int \frac{1}{25 x} d x - \int \frac{x}{25 ( x ^{2} + 25 )} d x)

\int \frac{1}{25 x} d x = \frac{1}{25} ln ∣ x ∣

\int \frac{x}{25 ( x ^{2} + 25 )} d x = \frac{1}{50} ln x^{2} + 25

= 13 (\frac{1}{25} ln ∣ x ∣ - \frac{1}{50} ln x^{2} + 25)

Füge eine Konstante zur Lösung hinzu

= 13 (\frac{1}{25} ln ∣ x ∣ - \frac{1}{50} ln x^{2} + 25) + C

Graph

Beliebte Beispiele

integral from 3 to 11 of 1/(sqrt(2x+3))

\int_{3}^{11} \frac{1}{2 x + 3} d x

t a y l or x^{\frac{9}{6}}

derivative f(x)=-10x^2+1760x-50000

d er i v a t i v e f (x) = - 10 x^{2} + 1760 x - 50000

derivative f(t)=9t-2t^2

d er i v a t i v e f (t) = 9 t - 2 t^{2}

y^{''}-2y^'+y=3e^tcos(t)

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{t} cos (t)