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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\int 2 x - 4 d x

\int (1 - 2 x) (3 + x) d x

in t e g r a l sec^{2} (t)

\int \frac{cos ( ln ( x + 1 ) )}{x + 1} d x

\int 5 x^{2} (x^{3} + 1)^{3} d x