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/(sqrt(x)-\sqrt[4]{x)}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{2 u}{u - 1} d u

Entferne die Konstante:

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

= 2 \cdot \int \frac{u}{u - 1} d u

Wende U-Substitution an

= 2 \cdot \int \frac{2 ( v ^{2} + 2 v + 1 )}{v} d v

Entferne die Konstante:

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

= 2 \cdot 2 \cdot \int \frac{v ^{2} + 2 v + 1}{v} d v

Multipliziere aus

\frac{v ^{2} + 2 v + 1}{v} : v + 2 + \frac{1}{v}

= 2 \cdot 2 \cdot \int v + 2 + \frac{1}{v} d v

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 \cdot 2 (\int v d v + \int 2 d v + \int \frac{1}{v} d v)

\int v d v = \frac{v ^{2}}{2}

\int 2 d v = 2 v

\int \frac{1}{v} d v = ln ∣ v ∣

= 2 \cdot 2 (\frac{v ^{2}}{2} + 2 v + ln ∣ v ∣)

Ersetze zurück

= 2 \cdot 2 \frac{( x - 1 ) ^{2}}{2} + 2 (x - 1) + ln x - 1

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral from 0 to 1 of 6e^{2x}

\int_{0}^{1} 6 e^{2 x} d x

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

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

vereinfachen (-a)/(x^2)+a/((x-2)^2)

s im pl i f y \frac{- a}{x ^{2}} + \frac{a}{( x - 2 ) ^{2}}

integral from 0 to 2 of 1/(4-2x)

\int_{0}^{2} \frac{1}{4 - 2 x} d x

integral from 1 to 5 of (2+3x-x^2)

\int_{1}^{5} (2 + 3 x - x^{2}) d x