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Beliebt Rechnen >

integral of x*sin(4x)

Lösung

\int x \cdot sin (4 x) d x

Lösung

- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x) + C

Schritte zur Lösung

\int x sin (4 x) d x

Wende die partielle Integration an

= - \frac{1}{4} x cos (4 x) - \int - \frac{1}{4} cos (4 x) d x

\int - \frac{1}{4} cos (4 x) d x = - \frac{1}{16} sin (4 x)

= - \frac{1}{4} x cos (4 x) - (- \frac{1}{16} sin (4 x))

Vereinfache

= - \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x) + C

Graph

Beliebte Beispiele

derivative of (-2x/(x^2+1))

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

integral of 12e^{3x-1}

\int 12 e^{3 x - 1} d x

integral of 6/((1-2x)^3)

\int \frac{6}{( 1 - 2 x ) ^{3}} d x

limit as x approaches 2 of sqrt(2x^2-4x)

x \to 2 lim (2 x^{2} - 4 x)

integral of (3x^2)/(sqrt(1-6x^3))

\int \frac{3 x ^{2}}{1 - 6 x ^{3}} d x