integral of (5x^2+3)cos(x)

Lösung

\int (5 x^{2} + 3) cos (x) d x

5 x^{2} sin (x) + 10 x cos (x) - 7 sin (x) + C

Schritte zur Lösung

\int (5 x^{2} + 3) cos (x) d x

Multipliziere aus

(5 x^{2} + 3) cos (x) : 5 x^{2} cos (x) + 3 cos (x)

= \int 5 x^{2} cos (x) + 3 cos (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 5 x^{2} cos (x) d x + \int 3 cos (x) d x

\int 5 x^{2} cos (x) d x = 5 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

\int 3 cos (x) d x = 3 sin (x)

= 5 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + 3 sin (x)

Vereinfache

5 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + 3 sin (x) : 5 x^{2} sin (x) + 10 x cos (x) - 7 sin (x)

= 5 x^{2} sin (x) + 10 x cos (x) - 7 sin (x)

Füge eine Konstante zur Lösung hinzu

= 5 x^{2} sin (x) + 10 x cos (x) - 7 sin (x) + C

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