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Beliebt Rechnen >

integral of (x^2-2)cos(2x)

Lösung

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

Lösung

\frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{5}{4} sin (2 x) + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int x^{2} cos (2 x) d x = \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{1}{4} sin (2 x)

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

= \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{1}{4} sin (2 x) - sin (2 x)

Addiere gleiche Elemente:

- \frac{1}{4} sin (2 x) - sin (2 x) = - \frac{5}{4} sin (2 x)

= \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{5}{4} sin (2 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{5}{4} sin (2 x) + C

Graph

Beliebte Beispiele

integral of (x^3+2x^2+3x+7)/(x^2-x-6)

\int \frac{x ^{3} + 2 x ^{2} + 3 x + 7}{x ^{2} - x - 6} d x

integral of 3x^2\sqrt[4]{9+3x^3}

\int 3 x^{2} 4 9 + 3 x^{3} d x

integral of (x^2+3x)e^x

\int (x^{2} + 3 x) e^{x} d x

integral of (x^4)/(3x^2+27)

\int \frac{x ^{4}}{3 x ^{2} + 27} d x

integral of (2x^2-2)sin(2x)

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