de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 19sin^2(xco)s^2x

Lösung

\int 19 sin^{2} (x co) s^{2} x d x

Lösung

\frac{19 s ^{2}}{8 c ^{2} o ^{2}} (2 c^{2} o^{2} x^{2} - 2 co x sin (2 co x) - cos (2 co x)) + C

Schritte zur Lösung

\int 19 sin^{2} (x co) s^{2} x d x

Entferne die Konstante:

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

= 19 s^{2} \cdot \int sin^{2} (co x) x d x

Wende U-Substitution an

= 19 s^{2} \cdot \int \frac{u sin ^{2} ( u )}{c ^{2} o ^{2}} d u

Entferne die Konstante:

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

= 19 s^{2} \frac{1}{c ^{2} o ^{2}} \cdot \int u sin^{2} (u) d u

Wende die partielle Integration an

= 19 s^{2} \frac{1}{c ^{2} o ^{2}} (\frac{1}{2} u (u - \frac{1}{2} sin (2 u)) - \int \frac{1}{2} (u - \frac{1}{2} sin (2 u)) d u)

\int \frac{1}{2} (u - \frac{1}{2} sin (2 u)) d u = \frac{1}{2} (\frac{u ^{2}}{2} + \frac{1}{4} cos (2 u))

= 19 s^{2} \frac{1}{c ^{2} o ^{2}} (\frac{1}{2} u (u - \frac{1}{2} sin (2 u)) - \frac{1}{2} (\frac{u ^{2}}{2} + \frac{1}{4} cos (2 u)))

Setze in

u = co x

ein

= 19 s^{2} \frac{1}{c ^{2} o ^{2}} (\frac{1}{2} co x (co x - \frac{1}{2} sin (2 co x)) - \frac{1}{2} (\frac{( co x ) ^{2}}{2} + \frac{1}{4} cos (2 co x)))

Vereinfache

19 s^{2} \frac{1}{c ^{2} o ^{2}} (\frac{1}{2} co x (co x - \frac{1}{2} sin (2 co x)) - \frac{1}{2} (\frac{( co x ) ^{2}}{2} + \frac{1}{4} cos (2 co x))) : \frac{19 s ^{2}}{8 c ^{2} o ^{2}} (2 c^{2} o^{2} x^{2} - 2 co x sin (2 co x) - cos (2 co x))

= \frac{19 s ^{2}}{8 c ^{2} o ^{2}} (2 c^{2} o^{2} x^{2} - 2 co x sin (2 co x) - cos (2 co x))

Füge eine Konstante zur Lösung hinzu

= \frac{19 s ^{2}}{8 c ^{2} o ^{2}} (2 c^{2} o^{2} x^{2} - 2 co x sin (2 co x) - cos (2 co x)) + C

Graph

Beliebte Beispiele

integral from-pi to pi of sin(3x)sin(3x)

derivative y= 1/3 x^{3/2}

(\partial)/(\partial x)(2x^2+2y^2)

derivative of x/(sqrt(9-4x))

y^{''}+9y=-24sin(3t)