integral of 1/2 xsinh(2x)

Lösung

\int \frac{1}{2} x sinh (2 x) d x

\frac{1}{2} (\frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x)) + C

Schritte zur Lösung

\int \frac{1}{2} x sinh (2 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 sinh (2 x) d x

Wende die partielle Integration an

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

\int \frac{1}{2} cosh (2 x) d x = \frac{1}{4} sinh (2 x)

= \frac{1}{2} (\frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (\frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x)) + C

\int (4 x^{2} - 5 x + 1) d x

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

\int (x^{2} - 6 x + 10) d x

\int sin^{2} (10 t) sec^{4} (10 t) d t

\int \frac{x ^{2}}{( x ^{2} - 1 ) ^{5}} d x