de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x-5)/(x^2+2x-3)

Lösung

\int \frac{x - 5}{x ^{2} + 2 x - 3} d x

Lösung

\frac{1}{2} ln x^{2} + 2 x - 3 + \frac{1}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) + \frac{5}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) + C

Schritte zur Lösung

\int \frac{x - 5}{x ^{2} + 2 x - 3} d x

Multipliziere aus

\frac{x - 5}{x ^{2} + 2 x - 3} : \frac{x}{x ^{2} + 2 x - 3} - \frac{5}{x ^{2} + 2 x - 3}

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{x}{x ^{2} + 2 x - 3} d x - \int \frac{5}{x ^{2} + 2 x - 3} d x

\int \frac{x}{x ^{2} + 2 x - 3} d x = \frac{1}{2} ln x^{2} + 2 x - 3 + \frac{1}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1)

\int \frac{5}{x ^{2} + 2 x - 3} d x = - \frac{5}{4} (ln \frac{x + 1}{2} + 1 - ln \frac{x + 1}{2} - 1)

= \frac{1}{2} ln x^{2} + 2 x - 3 + \frac{1}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) - (- \frac{5}{4} (ln \frac{x + 1}{2} + 1 - ln \frac{x + 1}{2} - 1))

Vereinfache

\frac{1}{2} ln x^{2} + 2 x - 3 + \frac{1}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) - (- \frac{5}{4} (ln \frac{x + 1}{2} + 1 - ln \frac{x + 1}{2} - 1)) : \frac{1}{2} ln x^{2} + 2 x - 3 + \frac{1}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) + \frac{5}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1)

= \frac{1}{2} ln x^{2} + 2 x - 3 + \frac{1}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) + \frac{5}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 2 x - 3 + \frac{1}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) + \frac{5}{4} (ln \frac{1}{2} (x + 1) + 1 - ln \frac{1}{2} (x + 1) - 1) + C

Graph

Beliebte Beispiele

tangent f(x)= 3/(5x+2),\at x=-1

t an g e n t f (x) = \frac{3}{5 x + 2}, at x = - 1

integral of (2x+1)^{5/6}

\int (2 x + 1)^{\frac{5}{6}} d x

(\partial)/(\partial x)(32x+13y+90)

\frac{\partial}{\partial x} (32 x + 13 y + 90)

d/(dt)(ln(a+{v}(t)t))

\frac{d}{d t} (ln (a + v (t) t))

derivative of (-1^nx^{2n})

\frac{d}{d x} ((- 1)^{n} x^{2 n})