integral of y^2cosh(7y)

Lösung

\int y^{2} cosh (7 y) d y

\frac{1}{343} (49 y^{2} sinh (7 y) - 2 (7 y cosh (7 y) - sinh (7 y))) + C

Schritte zur Lösung

\int y^{2} cosh (7 y) d y

Wende U-Substitution an

= \int \frac{u ^{2} cosh ( u )}{343} d u

Entferne die Konstante:

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

= \frac{1}{343} \cdot \int u^{2} cosh (u) d u

Wende die partielle Integration an

= \frac{1}{343} (u^{2} sinh (u) - \int 2 u sinh (u) d u)

\int 2 u sinh (u) d u = 2 (u cosh (u) - sinh (u))

= \frac{1}{343} (u^{2} sinh (u) - 2 (u cosh (u) - sinh (u)))

Setze in

u = 7 y

ein

= \frac{1}{343} ((7 y)^{2} sinh (7 y) - 2 (7 y cosh (7 y) - sinh (7 y)))

Vereinfache

\frac{1}{343} ((7 y)^{2} sinh (7 y) - 2 (7 y cosh (7 y) - sinh (7 y))) : \frac{1}{343} (49 y^{2} sinh (7 y) - 2 (7 y cosh (7 y) - sinh (7 y)))

= \frac{1}{343} (49 y^{2} sinh (7 y) - 2 (7 y cosh (7 y) - sinh (7 y)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{343} (49 y^{2} sinh (7 y) - 2 (7 y cosh (7 y) - sinh (7 y))) + C

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