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+1)/(xsqrt(x-4))

Lösung

\int \frac{x + 1}{x x - 4} d x

Lösung

2 x - 4 + arctan (\frac{1}{2} x - 4) + C

Schritte zur Lösung

\int \frac{x + 1}{x x - 4} d x

Multipliziere aus

\frac{x + 1}{x x - 4} : \frac{1}{x - 4} + \frac{1}{x x - 4}

= \int \frac{1}{x - 4} + \frac{1}{x 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}{x - 4} d x + \int \frac{1}{x x - 4} d x

\int \frac{1}{x - 4} d x = 2 x - 4

\int \frac{1}{x x - 4} d x = arctan (\frac{1}{2} x - 4)

= 2 x - 4 + arctan (\frac{1}{2} x - 4)

Füge eine Konstante zur Lösung hinzu

= 2 x - 4 + arctan (\frac{1}{2} x - 4) + C

Graph

Beliebte Beispiele

integral of (x+3)cos(x)

\int (x + 3) cos (x) d x

integral of sec^2(θ)-sin(θ)

\int sec^{2} (θ) - sin (θ) d θ

integral of (x 3/2+2x+1)

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

integral of 1/(sqrt(x))+(xsqrt(x))/3

\int \frac{1}{x} + \frac{x x}{3} d x

integral of 2/(xsqrt(x^2-16))

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