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Beliebt Rechnen >

integral of-x^2cos(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int x^{2} cos (x) d x

Wende die partielle Integration an

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

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

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

Vereinfache

- (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) : - x^{2} sin (x) - 2 x cos (x) + 2 sin (x)

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

inverselaplace (2a+b)/((s+1))

in v erse l a pl a ce \frac{2 a + b}{( s + 1 )}

integral of 20+75e^{-x/(50)}

\int 20 + 75 e^{- \frac{x}{50}} d x

t an g e n t 5 x^{2}

sum from n=1 to infinity of (-3)^{3n-1}

n = 1 \sum \infty (- 3)^{3 n - 1}

derivative of ln((x^3+1/(x^2+1)))

\frac{d}{d x} (ln (\frac{x ^{3} + 1}{x ^{2} + 1}))