integral of x^6cos(x)

Lösung

\int x^{6} cos (x) d x

x^{6} sin (x) - 6 (- x^{5} cos (x) + 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))))) + C

Schritte zur Lösung

\int x^{6} cos (x) d x

Wende die partielle Integration an

= x^{6} sin (x) - \int 6 x^{5} sin (x) d x

\int 6 x^{5} sin (x) d x = 6 (- x^{5} cos (x) + 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))))

= x^{6} sin (x) - 6 (- x^{5} cos (x) + 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))))

Füge eine Konstante zur Lösung hinzu

= x^{6} sin (x) - 6 (- x^{5} cos (x) + 5 (x^{4} sin (x) - 4 (- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))))) + C

d er i v a t i v e ln (cos (5 x))

\frac{\partial}{\partial x} ((e^{x^{2}} + e^{y^{2}})^{2})

\int \frac{1}{sin ( \frac{x}{2} )} d x

\int x^{2} ln (100) d x

d er i v a t i v e ln (4 - x^{2})