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Beliebt Rechnen >

integral of sqrt(1+(sinh(x))^2)

Lösung

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

Lösung

sinh (x) + C

Schritte zur Lösung

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

Vereinfache

1 + (sinh (x))^{2} : cosh^{2} (x)

= \int cosh^{2} (x) d x

cosh^{2} (x) = (cosh (x)),

angenommen

cosh (x) \geq 0

= \int cosh (x) d x

Nutze das gemeinsame Integral :

\int cosh (x) d x = sinh (x)

= sinh (x)

Füge eine Konstante zur Lösung hinzu

= sinh (x) + C

Graph

Beliebte Beispiele

integral of 2e^{-2y}

\int 2 e^{- 2 y} d y

derivative of e^{{g}(x(x^3)-2})

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

y^{''}+4y^'+6y=0,y(0)=-4,y^'(0)=-1

y^{^{''}} + 4 y^{^{'}} + 6 y = 0, y (0) = - 4, y^{^{'}} (0) = - 1

inverselaplace (x+1)/(x^2-4x)

in v erse l a pl a ce \frac{x + 1}{x ^{2} - 4 x}

integral of csc^2(x)+7

\int csc^{2} (x) + 7 d x