integral of sin(x)sinh(x)

Lösung

\int sin (x) sinh (x) d x

- \frac{cos ( x ) sinh ( x )}{2} + \frac{sin ( x ) cosh ( x )}{2} + C

Schritte zur Lösung

\int sin (x) sinh (x) d x

Wende die partielle Integration an

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= - sinh (x) cos (x) - (- (cosh (x) sin (x) - \int sinh (x) sin (x) d x))

Deshalb

\int sinh (x) sin (x) d x = - sinh (x) cos (x) - (- (cosh (x) sin (x) - \int sinh (x) sin (x) d x))

Isoliere

\int sinh (x) sin (x) d x

= - \frac{cos ( x ) sinh ( x )}{2} + \frac{sin ( x ) cosh ( x )}{2}

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ( x ) sinh ( x )}{2} + \frac{sin ( x ) cosh ( x )}{2} + C

in t e g r a l x^{2} e^{- x}

\int \frac{x ^{2}}{x + 9} d x

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

\int (\frac{4}{x ^{3}} + 6 x) d x

\int x \cdot sin (6 x) d x