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

Lösung

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

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

Schritte zur Lösung

\int \frac{1 + cos ( x )}{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 1 + cos (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

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

\int 1 d x = x

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

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

Füge eine Konstante zur Lösung hinzu

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

n = 3 \sum \infty - \frac{5}{n ^{1.01}}

d er i v a t i v e f (x) = 7 x^{3} - 5 x + 8

d er i v a t i v e cos (3 t)

\frac{d}{d x} (\frac{10 x}{( x ^{2} + 1 ) ^{2}})

\frac{d y}{d t} = (t + y)^{2} - 1