integral (1+2cos(x))^2

Lösung

integral

(1 + 2 cos (x))^{2}

3 x + 4 sin (x) + sin (2 x) + C

Schritte zur Lösung

\int (1 + 2 cos (x))^{2} d x

Multipliziere aus

(1 + 2 cos (x))^{2} : 1 + 4 cos (x) + 4 cos^{2} (x)

= \int 1 + 4 cos (x) + 4 cos^{2} (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 1 d x + \int 4 cos (x) d x + \int 4 cos^{2} (x) d x

\int 1 d x = x

\int 4 cos (x) d x = 4 sin (x)

\int 4 cos^{2} (x) d x = 2 x + sin (2 x)

= x + 4 sin (x) + 2 x + sin (2 x)

Vereinfache

= 3 x + 4 sin (x) + sin (2 x)

Füge eine Konstante zur Lösung hinzu

= 3 x + 4 sin (x) + sin (2 x) + C

in t e g r a l (2 x^{2})^{\frac{1}{3}}

in t e g r a l sin^{7} (x)

in t e g r a l \frac{( x + 5 )}{( x ^{2} + 8 x + 17 )}

in t e g r a l - 3 y^{2}

in t e g r a l - 2 e^{- x}