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Beliebt Rechnen >

integral of x/2 (e^x-e^{-x})

Lösung

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

Lösung

x cosh (x) - sinh (x) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int 2 cosh (x) d x = 2 sinh (x)

= \frac{1}{2} (2 x cosh (x) - 2 sinh (x))

Vereinfache

\frac{1}{2} (2 x cosh (x) - 2 sinh (x)) : x cosh (x) - sinh (x)

= x cosh (x) - sinh (x)

Füge eine Konstante zur Lösung hinzu

= x cosh (x) - sinh (x) + C

Graph

Beliebte Beispiele

integral of sec^{15}(x)tan(x)

\int sec^{15} (x) tan (x) d x

integral of x^3(x^2+1)^{14}

\int x^{3} (x^{2} + 1)^{14} d x

integral of 3/(2x^2+50)

\int \frac{3}{2 x ^{2} + 50} d x

integral of (10)/(\sqrt[3]{x)}

\int \frac{10}{3 x} d x

integral of (x^3-3x+2)/(x(x^2+2x+1))

\int \frac{x ^{3} - 3 x + 2}{x ( x ^{2} + 2 x + 1 )} d x