integral of (cos^3(3x)-cos(3x))

Lösung

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

- \frac{1}{9} sin^{3} (3 x) + C

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos^{3} (3 x) d x - \int cos (3 x) d x

\int cos^{3} (3 x) d x = \frac{1}{3} (sin (3 x) - \frac{sin ^{3} ( 3 x )}{3})

\int cos (3 x) d x = \frac{1}{3} sin (3 x)

= \frac{1}{3} (sin (3 x) - \frac{sin ^{3} ( 3 x )}{3}) - \frac{1}{3} sin (3 x)

Vereinfache

\frac{1}{3} (sin (3 x) - \frac{sin ^{3} ( 3 x )}{3}) - \frac{1}{3} sin (3 x) : - \frac{1}{9} sin^{3} (3 x)

= - \frac{1}{9} sin^{3} (3 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{9} sin^{3} (3 x) + C

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

\int (3 e^{x} + \frac{4}{x}) d x

\int (4 - 2 x)^{3} d x

\int (1 + \frac{1}{x}) (1 - \frac{4}{x ^{2}}) d x

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