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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of t/((t^2+1)^2)

\int \frac{t}{( t ^{2} + 1 ) ^{2}} d t

integral of 1/(sin(5x))

\int \frac{1}{sin ( 5 x )} d x

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

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

integral of (5.4145)/(sqrt(1+0.91t))

\int \frac{5.4145}{1 + 0.91 t} d t

integral of (cos^3(y))/(1+cos(2y))

\int \frac{cos ^{3} ( y )}{1 + cos ( 2 y )} d y