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Beliebt Rechnen >

integral of xsin(ax)

Lösung

\int x sin (a x) d x

Lösung

- \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x) + C

Schritte zur Lösung

\int x sin (a x) d x

Wende die partielle Integration an

= - \frac{1}{a} x cos (a x) - \int - \frac{1}{a} cos (a x) d x

\int - \frac{1}{a} cos (a x) d x = - \frac{1}{a ^{2}} sin (a x)

= - \frac{1}{a} x cos (a x) - (- \frac{1}{a ^{2}} sin (a x))

Vereinfache

= - \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x) + C

Graph

Beliebte Beispiele

integral of ln(cos(x))

\int ln (cos (x)) d x

y^{^{'}} = 1 - \frac{y}{100}

t an g e n t sin (x)

derivative 5(x^{2n-1})*(2x^{3n+1})^2

d er i v a t i v e 5 (x^{2 n - 1}) \cdot (2 x^{3 n + 1})^{2}

f (x) = x e^{\frac{1}{x}}