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Beliebt Rechnen >

integral of x*sin(ax)

Lösung

\int x \cdot 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

x^2y^{''}+xy^'-y= 1/(x+1)

x^{2} y^{^{''}} + x y^{^{'}} - y = \frac{1}{x + 1}

limit as x approaches 1-of x/(ln(x))

x \to 1 - lim (\frac{x}{ln ( x )})

integral of ((x+3))/(2x^3-8x)

\int \frac{( x + 3 )}{2 x ^{3} - 8 x} d x

(\partial)/(\partial y)(xe^z)

\frac{\partial}{\partial y} (x e^{z})

derivative of sqrt(r^2-x^2)

\frac{d}{d x} (r^{2} - x^{2})