integral of (()(sin(2t)))^2

Lösung

\int (\frac{d}{d t} (sin (2 t)))^{2} d t

t \frac{d}{d t} (sin (2 t))^{2} + 8 (- \frac{1}{4} t cos (4 t) + \frac{1}{16} sin (4 t)) + C

Schritte zur Lösung

\int \frac{d}{d t} (sin (2 t))^{2} d t

Wende die partielle Integration an

= t \frac{d}{d t} (sin (2 t))^{2} - \int - 8 t sin (4 t) d t

\int - 8 t sin (4 t) d t = - 8 (- \frac{1}{4} t cos (4 t) + \frac{1}{16} sin (4 t))

= t \frac{d}{d t} (sin (2 t))^{2} - (- 8 (- \frac{1}{4} t cos (4 t) + \frac{1}{16} sin (4 t)))

Vereinfache

= t \frac{d}{d t} (sin (2 t))^{2} + 8 (- \frac{1}{4} t cos (4 t) + \frac{1}{16} sin (4 t))

Füge eine Konstante zur Lösung hinzu

= t \frac{d}{d t} (sin (2 t))^{2} + 8 (- \frac{1}{4} t cos (4 t) + \frac{1}{16} sin (4 t)) + C

f a c t or \frac{2550}{17000}

f a c t or 27 x^{4} + 40 x^{4} + 3 0^{2}

f a c t or 3 - (4^{\frac{2}{5}})

f a c t or \frac{x ^{2} - 36}{6 - x}

f a c t or 5 (e^{2 x} cos (x))