de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of xsqrt(1+2x^2)

Lösung

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

Lösung

\frac{1}{6} (1 + 2 x^{2})^{\frac{3}{2}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int u d u

Wende die Potenzregel an

= \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = 1 + 2 x^{2}

ein

= \frac{1}{4} \cdot \frac{2}{3} (1 + 2 x^{2})^{\frac{3}{2}}

Vereinfache

\frac{1}{4} \cdot \frac{2}{3} (1 + 2 x^{2})^{\frac{3}{2}} : \frac{1}{6} (1 + 2 x^{2})^{\frac{3}{2}}

= \frac{1}{6} (1 + 2 x^{2})^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{6} (1 + 2 x^{2})^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of 3/(x^7)

\int \frac{3}{x ^{7}} d x

limit as x approaches infinity of e^{-5}

x \to \infty lim (e^{- 5})

integral of (sin^4(x))/(cos^2(x))

\int \frac{sin ^{4} ( x )}{cos ^{2} ( x )} d x

normal x-10y=1,(-9,3)

n or ma l x - 10 y = 1, (- 9, 3)

(d^{10})/(dx^{10)}(x^{10})

\frac{d ^{10}}{d x ^{10}} (x^{10})