integral of (x+1)cos(nx)

Lösung

\int (x + 1) cos (n x) d x

\frac{1}{n} sin (n x) (x + 1) + \frac{1}{n ^{2}} cos (n x) + C

Schritte zur Lösung

\int (x + 1) cos (n x) d x

Wende die partielle Integration an

= \frac{1}{n} sin (n x) (x + 1) - \int \frac{1}{n} sin (n x) d x

\int \frac{1}{n} sin (n x) d x = - \frac{1}{n ^{2}} cos (n x)

= \frac{1}{n} sin (n x) (x + 1) - (- \frac{1}{n ^{2}} cos (n x))

Vereinfache

= \frac{1}{n} sin (n x) (x + 1) + \frac{1}{n ^{2}} cos (n x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{n} sin (n x) (x + 1) + \frac{1}{n ^{2}} cos (n x) + C

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

\int n x d x

\int 9 x^{8} e^{7 x^{9}} d x

\int \frac{x ^{5}}{20} d x

\int 6 x e^{x^{2}} sin (e^{x^{2}}) d x