de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of sqrt(cos(x))*sin^3(x)

Lösung

\int cos (x) \cdot sin^{3} (x) d x

Lösung

- \frac{2}{3} cos^{\frac{3}{2}} (x) + \frac{2}{7} cos^{\frac{7}{2}} (x) + C

Schritte zur Lösung

\int cos (x) sin^{3} (x) d x

Wende U-Substitution an

= \int - u (1 - u^{2}) d u

Entferne die Konstante:

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

= - \int u (1 - u^{2}) d u

Multipliziere aus

u (1 - u^{2}) : u - u^{\frac{5}{2}}

= - \int u - u^{\frac{5}{2}} 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

= - (\int u d u - \int u^{\frac{5}{2}} d u)

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

\int u^{\frac{5}{2}} d u = \frac{2}{7} u^{\frac{7}{2}}

= - (\frac{2}{3} u^{\frac{3}{2}} - \frac{2}{7} u^{\frac{7}{2}})

Setze in

u = cos (x)

ein

= - (\frac{2}{3} cos^{\frac{3}{2}} (x) - \frac{2}{7} cos^{\frac{7}{2}} (x))

Vereinfache

= - \frac{2}{3} cos^{\frac{3}{2}} (x) + \frac{2}{7} cos^{\frac{7}{2}} (x)

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{3} cos^{\frac{3}{2}} (x) + \frac{2}{7} cos^{\frac{7}{2}} (x) + C

Graph

Beliebte Beispiele

integral from 0 to 1 of (-7y)/(e^{2y)}

\int_{0}^{1} \frac{- 7 y}{e ^{2 y}} d y

laplacetransform e^{-10t}

l a pl a ce t r an s f or m e^{- 10 t}

integral from 0 to pi of cos^2(x)sin(x)

\int_{0}^{π} cos^{2} (x) sin (x) d x

derivative 2cos^3(x)

d er i v a t i v e 2 cos^{3} (x)

integral of (sqrt(8x)-2x)

\int (8 x - 2 x) d x