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

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{5 x + 1}{9 x ^{2} + 6 x + 3} d x

\int x^{3} cos (7 x) d x

\int \frac{x ^{2}}{3 5 + x ^{3}} d x

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

\int x (x^{2} + 5)^{7} d x