integral of sin^{10}(x)

Lösung

\int sin^{10} (x) d x

- \frac{cos ( x ) sin ^{9} ( x )}{10} + \frac{9}{10} (- \frac{cos ( x ) sin ^{7} ( x )}{8} + \frac{7}{8} (- \frac{cos ( x ) sin ^{5} ( x )}{6} + \frac{5}{6} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x))))) + C

Schritte zur Lösung

\int sin^{10} (x) d x

Wende integrale Reduktion an

= - \frac{cos ( x ) sin ^{9} ( x )}{10} + \frac{9}{10} \cdot \int sin^{8} (x) d x

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

= - \frac{cos ( x ) sin ^{9} ( x )}{10} + \frac{9}{10} (- \frac{cos ( x ) sin ^{7} ( x )}{8} + \frac{7}{8} (- \frac{cos ( x ) sin ^{5} ( x )}{6} + \frac{5}{6} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x)))))

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ( x ) sin ^{9} ( x )}{10} + \frac{9}{10} (- \frac{cos ( x ) sin ^{7} ( x )}{8} + \frac{7}{8} (- \frac{cos ( x ) sin ^{5} ( x )}{6} + \frac{5}{6} (- \frac{1}{4} sin^{3} (x) cos (x) + \frac{3}{8} (x - \frac{1}{2} sin (2 x))))) + C

t an g e n t f (x) = \frac{4}{x ^{2}}, (1, 4)

d er i v a t i v e f (x) = (3 - e^{- 4 x})^{4}

a re a 29 - 11 x, 1 - x^{2}

\frac{d}{d x} (7 x - \frac{8}{x})

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 2 e^{x}