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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

\int 1 d x = x

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

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

Vereinfache

x + \frac{1}{2} (x - \frac{1}{2} sin (2 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 of ln((x-4^3))

\frac{d}{d x} (ln ((x - 4)^{3}))

integral of x*sqrt(x^2+5)

\int x \cdot x^{2} + 5 d x

t a y l or ln (4 - x)

(\partial)/(\partial z)(ln(1+x^2+e^y+z))

\frac{\partial}{\partial z} (ln (1 + x^{2} + e^{y} + z))

limit as x approaches 0 of 1/(1-e^{-x)}

x \to 0 lim (\frac{1}{1 - e ^{- x}})