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

Lösung

integral

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

\frac{1}{8} (6 x + sin (2 x)) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int cos^{2} (x) + 1 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

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

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

\int 1 d x = x

= \frac{1}{2} (\frac{1}{2} (x + \frac{1}{2} sin (2 x)) + x)

Vereinfache

\frac{1}{2} (\frac{1}{2} (x + \frac{1}{2} sin (2 x)) + x) : \frac{1}{8} (6 x + sin (2 x))

= \frac{1}{8} (6 x + sin (2 x))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{8} (6 x + sin (2 x)) + C

in t e g r a l \frac{- x}{3}

in t e g r a l e^{x} \cdot x^{3}

in t e g r a l 2 lo g_{10} (\frac{1}{( 2 x + 1 )})

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

in t e g r a l \frac{1}{x w \cdot r t x}