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Beliebt Rechnen >

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

Lösung

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

Lösung

- cos^{2} (2 x) cos (x) + \frac{1}{5} cos (5 x) + \frac{1}{3} cos (3 x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= - cos^{2} (2 x) cos (x) - \int 2 sin (4 x) cos (x) d x

\int 2 sin (4 x) cos (x) d x = - \frac{1}{5} cos (5 x) - \frac{1}{3} cos (3 x)

= - cos^{2} (2 x) cos (x) - (- \frac{1}{5} cos (5 x) - \frac{1}{3} cos (3 x))

Vereinfache

= - cos^{2} (2 x) cos (x) + \frac{1}{5} cos (5 x) + \frac{1}{3} cos (3 x)

Füge eine Konstante zur Lösung hinzu

= - cos^{2} (2 x) cos (x) + \frac{1}{5} cos (5 x) + \frac{1}{3} cos (3 x) + C

Graph

Beliebte Beispiele

integral of 20sin(x)

\int 20 sin (x) d x

integral of (sin(46x))/(1+cos^2(46x))

\int \frac{sin ( 46 x )}{1 + cos ^{2} ( 46 x )} d x

integral of (x^7-5x)/(x^6)

\int \frac{x ^{7} - 5 x}{x ^{6}} d x

integral of 2xsin(npix)

\int 2 x sin (nπ x) d x

integral of 1/(sqrt(x+6x^2))

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