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Beliebt Rechnen >

integral of-xcos(x)+x

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral from 0 to l of cos((piy)/(2l))

\int_{0}^{l} cos (\frac{π y}{2 l}) d y

derivative g(t)=t-4/(t^3)

d er i v a t i v e g (t) = t - \frac{4}{t ^{3}}

f (t) = 2 e^{2 t}

derivative of (x+1/2)

\frac{d}{d x} (\frac{x + 1}{2})

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

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