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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{2} ln ∣ 1 + 2 sin (x) ∣ + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Setze in

u = 1 + 2 sin (x)

ein

= \frac{1}{2} ln ∣ 1 + 2 sin (x) ∣

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of e^{ln(x^2})

\frac{d}{d x} (e^{l n (x^{2})})

derivative of x/((1-x^2))

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

derivative f(x)= 7/(r^3)

d er i v a t i v e f (x) = \frac{7}{r ^{3}}

derivative f(x)=7x^{3/2}

d er i v a t i v e f (x) = 7 x^{\frac{3}{2}}

(\partial)/(\partial x)(cos(7x^2y-3xy^3))

\frac{\partial}{\partial x} (cos (7 x^{2} y - 3 x y^{3}))