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)/(sqrt(2x+1))

Lösung

\int \frac{x + 1}{2 x + 1} d x

Lösung

\frac{1}{3} x 2 x + 1 + \frac{2}{3} 2 x + 1 + C

Schritte zur Lösung

\int \frac{x + 1}{2 x + 1} d x

Multipliziere aus

\frac{x + 1}{2 x + 1} : \frac{x}{2 x + 1} + \frac{1}{2 x + 1}

= \int \frac{x}{2 x + 1} + \frac{1}{2 x + 1} 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{x}{2 x + 1} d x + \int \frac{1}{2 x + 1} d x

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

\int \frac{1}{2 x + 1} d x = 2 x + 1

= \frac{1}{3} (x - 1) 2 x + 1 + 2 x + 1

Vereinfache

\frac{1}{3} (x - 1) 2 x + 1 + 2 x + 1 : \frac{1}{3} x 2 x + 1 + \frac{2}{3} 2 x + 1

= \frac{1}{3} x 2 x + 1 + \frac{2}{3} 2 x + 1

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x 2 x + 1 + \frac{2}{3} 2 x + 1 + C

Graph

Beliebte Beispiele

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

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

integral of (x^{1.8}+7x^{2.5})

\int (x^{1.8} + 7 x^{2.5}) d x

integral of (4u-6)sqrt(u^2-3u)

\int (4 u - 6) u^{2} - 3 u d u

integral of x(x+4)^{1/4}

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

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

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