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Beliebt Rechnen >

integral of (cosh(x))/(2+3sinh(x))

Lösung

\int \frac{cosh ( x )}{2 + 3 sinh ( x )} d x

Lösung

\frac{1}{3} ln ∣ 2 + 3 sinh (x) ∣ + C

Schritte zur Lösung

\int \frac{cosh ( x )}{2 + 3 sinh ( x )} d x

Wende U-Substitution an

= \int \frac{1}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Setze in

u = 2 + 3 sinh (x)

ein

= \frac{1}{3} ln ∣ 2 + 3 sinh (x) ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} ln ∣ 2 + 3 sinh (x) ∣ + C

Graph

Beliebte Beispiele

derivative of (sec(x)/(1+sec(x)))

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(\partial)/(\partial x)(x^2+3yz+4xy)

\frac{\partial}{\partial x} (x^{2} + 3 yz + 4 x y)

y^'=(xy^'+y)y^1985

y^{^{'}} = (x y^{^{'}} + y) y^{1} 985