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Beliebt Rechnen >

integral of csch(1/2)xcoth(1/2)x

Lösung

\int csch (\frac{1}{2}) x coth (\frac{1}{2}) x d x

Lösung

\frac{6 e ^{2} e + 2 e ^{\frac{7}{2}} + 6 e ^{\frac{3}{2}} + 2 e}{( e ^{2} - 1 ) ^{2}} \cdot \frac{x ^{3}}{3} + C

Schritte zur Lösung

\int csch (\frac{1}{2}) x coth (\frac{1}{2}) x d x

Entferne die Konstante:

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

= csch (\frac{1}{2}) coth (\frac{1}{2}) \cdot \int xx d x

csch (\frac{1}{2}) coth (\frac{1}{2}) = \frac{6 e ^{2} e + 2 e ^{\frac{7}{2}} + 6 e ^{\frac{3}{2}} + 2 e}{( e ^{2} - 1 ) ^{2}}

= \frac{6 e ^{2} e + 2 e ^{\frac{7}{2}} + 6 e ^{\frac{3}{2}} + 2 e}{( e ^{2} - 1 ) ^{2}} \cdot \int xx d x

Vereinfache

xx : x^{2}

= \frac{6 e ^{2} e + 2 e ^{\frac{7}{2}} + 6 e ^{\frac{3}{2}} + 2 e}{( e ^{2} - 1 ) ^{2}} \cdot \int x^{2} d x

Wende die Potenzregel an

= \frac{6 e ^{2} e + 2 e ^{\frac{7}{2}} + 6 e ^{\frac{3}{2}} + 2 e}{( e ^{2} - 1 ) ^{2}} \cdot \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{6 e ^{2} e + 2 e ^{\frac{7}{2}} + 6 e ^{\frac{3}{2}} + 2 e}{( e ^{2} - 1 ) ^{2}} \cdot \frac{x ^{3}}{3} + C

Graph

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