integral of cos^6(θ)

Lösung

\int cos^{6} (θ) d θ

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

Schritte zur Lösung

\int cos^{6} (θ) d θ

Wende integrale Reduktion an

= \frac{sin ( θ ) cos ^{5} ( θ )}{6} + \frac{5}{6} \cdot \int cos^{4} (θ) d θ

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

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

Füge eine Konstante zur Lösung hinzu

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

t an g e n t f (x) = (x - x^{3}), at x = 1

\frac{d}{d x} (\frac{1}{4} e^{2 x})

\int (sin (3 x) + 3 cos (3 x))^{2} d x

\frac{\partial}{\partial x} (2 x y^{7} + x^{7} y^{9})

\int 6 tan (6 x) d x