integral of x(cos(x)-sin(x))

Lösung

\int x (cos (x) - sin (x)) d x

x sin (x) + x cos (x) + cos (x) - sin (x) + C

Schritte zur Lösung

\int x (cos (x) - sin (x)) d x

Wende die partielle Integration an

= x (sin (x) + cos (x)) - \int sin (x) + cos (x) d x

\int sin (x) + cos (x) d x = - cos (x) + sin (x)

= x (sin (x) + cos (x)) - (- cos (x) + sin (x))

Vereinfache

x (sin (x) + cos (x)) - (- cos (x) + sin (x)) : x sin (x) + x cos (x) + cos (x) - sin (x)

= x sin (x) + x cos (x) + cos (x) - sin (x)

Füge eine Konstante zur Lösung hinzu

= x sin (x) + x cos (x) + cos (x) - sin (x) + C

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

x \frac{d y}{d x} = y^{2}

t a y l or sin (4 x)

\int - \frac{e ^{4 x}}{4 x} d x

\int \frac{cos ( 4 x )}{2 + sin ( 4 x )} d x