integral of xcos((mpix)/2)

Lösung

\int x cos (\frac{mπ x}{2}) d x

\frac{2}{πm} x sin (\frac{πm x}{2}) + \frac{4}{π ^{2} m ^{2}} cos (\frac{πm x}{2}) + C

Schritte zur Lösung

\int x cos (\frac{mπ x}{2}) d x

Wende die partielle Integration an

= \frac{2}{πm} x sin (\frac{πm x}{2}) - \int \frac{2}{πm} sin (\frac{πm x}{2}) d x

\int \frac{2}{πm} sin (\frac{πm x}{2}) d x = - \frac{4}{π ^{2} m ^{2}} cos (\frac{πm x}{2})

= \frac{2}{πm} x sin (\frac{πm x}{2}) - (- \frac{4}{π ^{2} m ^{2}} cos (\frac{πm x}{2}))

Vereinfache

= \frac{2}{πm} x sin (\frac{πm x}{2}) + \frac{4}{π ^{2} m ^{2}} cos (\frac{πm x}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{2}{πm} x sin (\frac{πm x}{2}) + \frac{4}{π ^{2} m ^{2}} cos (\frac{πm x}{2}) + C

\frac{d}{d x} ((\frac{3}{5})^{x})

\int sec (t) (4 sec (t) + 7 tan (t)) d t

\frac{d}{d y} (y e^{x})

x \to - \infty lim (x^{- 2})

x^{2} y^{^{''}} + 7 x y^{^{'}} + 8 y = 0, y (1) = 0, y^{^{'}} (1) = - 5