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Beliebt Rechnen >

integral of sqrt(1+sin(2x))

Lösung

\int 1 + sin (2 x) d x

Lösung

sin (x) - cos (x) + C

Schritte zur Lösung

\int 1 + sin (2 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int (cos (x) + sin (x))^{2} d x

(cos (x) + sin (x))^{2} = ((cos (x) + sin (x))),

angenommen

(cos (x) + sin (x)) \geq 0

= \int cos (x) + sin (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) d x + \int sin (x) d x

\int cos (x) d x = sin (x)

\int sin (x) d x = - cos (x)

= sin (x) - cos (x)

Füge eine Konstante zur Lösung hinzu

= sin (x) - cos (x) + C

Graph

Beliebte Beispiele

tangent f(x)=x^2,\at x=7

t an g e n t f (x) = x^{2}, at x = 7

limit as h approaches 6 of (4h)/(h-6)

h \to 6 lim (\frac{4 h}{h - 6})

derivative of-tan(9x)

\frac{d}{d x} (- tan (9 x))

limit as x approaches 0 of [(2x+1)(x-3)]

x \to 0 lim ([(2 x + 1) (x - 3)])

derivative y=2x+5/x

d er i v a t i v e y = 2 x + \frac{5}{x}