integral of (x-1)cos(5x)

Lösung

\int (x - 1) cos (5 x) d x

\frac{1}{5} sin (5 x) (x - 1) + \frac{1}{25} cos (5 x) + C

Schritte zur Lösung

\int (x - 1) cos (5 x) d x

Wende die partielle Integration an

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

\int \frac{1}{5} sin (5 x) d x = - \frac{1}{25} cos (5 x)

= \frac{1}{5} sin (5 x) (x - 1) - (- \frac{1}{25} cos (5 x))

Vereinfache

= \frac{1}{5} sin (5 x) (x - 1) + \frac{1}{25} cos (5 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} sin (5 x) (x - 1) + \frac{1}{25} cos (5 x) + C

\int cos (\frac{t}{4}) d t

\int \frac{6}{x ln ^{3} ( 4 x )} d x

\int 12 (x^{4} + 4 x^{2} + 1)^{2} (x^{3} + 2 x) d x

\int 12 x^{11} d x

in t e g r a l rr θ \cdot 2 - 4 sin (θ)