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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of e^{-1/4 x}

\int e^{- \frac{1}{4} x} d x

integral of 24x+24x^2

\int 24 x + 24 x^{2} d x

integral of x^{1/2}+3

\int x^{\frac{1}{2}} + 3 d x

integral of (5x+6)/(x^2+x+1)

\int \frac{5 x + 6}{x ^{2} + x + 1} d x

integral of 18xe^{-9x}

\int 18 x e^{- 9 x} d x