de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 2xsqrt(4x-5)

Lösung

\int 2 x 4 x - 5 d x

Lösung

\frac{1}{30} (6 x + 5) (4 x - 5)^{\frac{3}{2}} + C

Schritte zur Lösung

\int 2 x 4 x - 5 d x

Entferne die Konstante:

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

= 2 \cdot \int x 4 x - 5 d x

Wende U-Substitution an

= 2 \cdot \int \frac{u ( u + 5 )}{16} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{16} \cdot \int u (u + 5) d u

Multipliziere aus

u (u + 5) : u^{\frac{3}{2}} + 5 u

= 2 \cdot \frac{1}{16} \cdot \int u^{\frac{3}{2}} + 5 u d u

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 \frac{1}{16} (\int u^{\frac{3}{2}} d u + \int 5 u d u)

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

\int 5 u d u = \frac{10}{3} u^{\frac{3}{2}}

= 2 \cdot \frac{1}{16} (\frac{2}{5} u^{\frac{5}{2}} + \frac{10}{3} u^{\frac{3}{2}})

Setze in

u = 4 x - 5

ein

= 2 \cdot \frac{1}{16} (\frac{2}{5} (4 x - 5)^{\frac{5}{2}} + \frac{10}{3} (4 x - 5)^{\frac{3}{2}})

Vereinfache

2 \cdot \frac{1}{16} (\frac{2}{5} (4 x - 5)^{\frac{5}{2}} + \frac{10}{3} (4 x - 5)^{\frac{3}{2}}) : \frac{1}{30} (6 x + 5) (4 x - 5)^{\frac{3}{2}}

= \frac{1}{30} (6 x + 5) (4 x - 5)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{30} (6 x + 5) (4 x - 5)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of 1/((z^2-2z+5)^2)

\int \frac{1}{( z ^{2} - 2 z + 5 ) ^{2}} d z

integral of (4x)/(sqrt(16-x^2))

\int \frac{4 x}{16 - x ^{2}} d x

integral of 3sec^2(3x)tan(3x)

\int 3 sec^{2} (3 x) tan (3 x) d x

integral of ((arcsin(ln(x))))/x

\int \frac{( arcsin ( ln ( x ) ) )}{x} d x

integral 1/(x^4)

in t e g r a l \frac{1}{x ^{4}}