integral of cos^3(7x)sin^{-2}(7x)

Lösung

\int cos^{3} (7 x) sin^{- 2} (7 x) d x

- \frac{1}{7} cos^{3} (7 x) cot (7 x) - \frac{3}{7} sin (7 x) + \frac{1}{7} sin^{3} (7 x) + C

Schritte zur Lösung

\int cos^{3} (7 x) sin^{- 2} (7 x) d x

Wende die partielle Integration an

= - \frac{1}{7} cos^{3} (7 x) cot (7 x) - \int 3 cos^{2} (7 x) sin (7 x) cot (7 x) d x

\int 3 cos^{2} (7 x) sin (7 x) cot (7 x) d x = \frac{3}{7} sin (7 x) - \frac{1}{7} sin^{3} (7 x)

= - \frac{1}{7} cos^{3} (7 x) cot (7 x) - (\frac{3}{7} sin (7 x) - \frac{1}{7} sin^{3} (7 x))

Vereinfache

= - \frac{1}{7} cos^{3} (7 x) cot (7 x) - \frac{3}{7} sin (7 x) + \frac{1}{7} sin^{3} (7 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{7} cos^{3} (7 x) cot (7 x) - \frac{3}{7} sin (7 x) + \frac{1}{7} sin^{3} (7 x) + C

x^{^{'}} = - x

\int (- 7 x) d x

\int_{- 2}^{3} \frac{5}{x ^{4}} d x

n = 1 \sum \infty 3

\int (x - sin (x)) d x