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Beliebt Rechnen >

integral of cos^2(x)+1

Lösung

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

Lösung

\frac{3}{2} x + \frac{1}{4} sin (2 x) + C

Schritte zur Lösung

\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

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

Vereinfache

\frac{1}{2} (x + \frac{1}{2} sin (2 x)) + x : \frac{3}{2} x + \frac{1}{4} sin (2 x)

= \frac{3}{2} x + \frac{1}{4} sin (2 x)

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} x + \frac{1}{4} sin (2 x) + C

Graph

Beliebte Beispiele

derivative y=-4log_{5}(x)

d er i v a t i v e y = - 4 lo g_{5} (x)

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\frac{d}{d x} (e^{3 x} + e^{x + e^{- 2 x}})

integral from 1 to e of t^2ln(t)

\int_{1}^{e} t^{2} ln (t) d t

derivative (x-3)/x

d er i v a t i v e \frac{x - 3}{x}

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\int \frac{1}{x ^{2} + 4 x + 2} d x