de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of sin^{18}(x)cos^3(x)

Lösung

\int sin^{18} (x) cos^{3} (x) d x

Lösung

\frac{sin ^{19} ( x )}{19} - \frac{sin ^{21} ( x )}{21} + C

Schritte zur Lösung

\int sin^{18} (x) cos^{3} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int (1 - sin^{2} (x)) cos (x) sin^{18} (x) d x

Wende U-Substitution an

= \int u^{18} (1 - u^{2}) d u

Multipliziere aus

u^{18} (1 - u^{2}) : u^{18} - u^{20}

= \int u^{18} - u^{20} 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^{18} d u - \int u^{20} d u

\int u^{18} d u = \frac{u ^{19}}{19}

\int u^{20} d u = \frac{u ^{21}}{21}

= \frac{u ^{19}}{19} - \frac{u ^{21}}{21}

Setze in

u = sin (x)

ein

= \frac{sin ^{19} ( x )}{19} - \frac{sin ^{21} ( x )}{21}

Füge eine Konstante zur Lösung hinzu

= \frac{sin ^{19} ( x )}{19} - \frac{sin ^{21} ( x )}{21} + C

Graph

Beliebte Beispiele

derivative g(x)=4x^2(x^3+5x)

d er i v a t i v e g (x) = 4 x^{2} (x^{3} + 5 x)

integral of (-8sec(x)tan(x)+5sec^2(x))

\int (- 8 sec (x) tan (x) + 5 sec^{2} (x)) d x

derivative of (2-7x^{3/2}^2)

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

y^{^{'}} + e^{x} y = 1

2x^{''}+4x^'+8x=0,x(0)=0,x^'(0)=1

2 x^{^{''}} + 4 x^{^{'}} + 8 x = 0, x (0) = 0, x^{^{'}} (0) = 1