integral of cos^8(x)

Lösung

\int cos^{8} (x) d x

\frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} (\frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x)))) + C

Schritte zur Lösung

\int cos^{8} (x) d x

Wende integrale Reduktion an

= \frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} \cdot \int cos^{6} (x) d x

\int cos^{6} (x) d x = \frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x)))

= \frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} (\frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x))))

Füge eine Konstante zur Lösung hinzu

= \frac{sin ( x ) cos ^{7} ( x )}{8} + \frac{7}{8} (\frac{sin ( x ) cos ^{5} ( x )}{6} + \frac{5}{6} (\frac{1}{4} cos^{3} (x) sin (x) + \frac{3}{8} (x + \frac{1}{2} sin (2 x)))) + C

d er i v a t i v e (x^{- 2} + x^{- 3}) (x^{5} - 2 x^{2})

x \to - 1 lim (x^{2} + 6)

d er i v a t i v e f (x) = 5 x + 9

y^{3} - (14 x + 6) + 3 x y^{2} y^{^{'}} = 0

\int_{0}^{1} 3^{4 x} d x