integral of cos^3(x)-1

Lösung

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

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

Schritte zur Lösung

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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

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

\int \frac{x ^{2} + 2 x + 3}{x ^{2} - 6 x + 8} d x

\int 1 + u d u

\int \frac{lo g _{e} ( x )}{x ^{2}} d x

\int \frac{1}{2 + 5 cos ( x )} d x