integral of x^3*cos(2x)

Lösung

\int x^{3} \cdot cos (2 x) d x

\frac{1}{2} x^{3} sin (2 x) - \frac{3}{2} (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x))) + C

Schritte zur Lösung

\int x^{3} cos (2 x) d x

Wende die partielle Integration an

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

\int \frac{3}{2} x^{2} sin (2 x) d x = \frac{3}{2} (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x)))

= \frac{1}{2} x^{3} sin (2 x) - \frac{3}{2} (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{3} sin (2 x) - \frac{3}{2} (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x))) + C

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

\int x 5 81 + x^{2} d x

\int e^{- 3 z} d z

\int 18 sec^{2} (x) tan^{5} (x) d x

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