integral of cos^3(5x)sin^{-2}(5x)

Lösung

\int cos^{3} (5 x) sin^{- 2} (5 x) d x

- \frac{1}{5} cos^{3} (5 x) cot (5 x) - \frac{3}{5} sin (5 x) + \frac{1}{5} sin^{3} (5 x) + C

Schritte zur Lösung

\int cos^{3} (5 x) sin^{- 2} (5 x) d x

Wende die partielle Integration an

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - \int 3 cos^{2} (5 x) sin (5 x) cot (5 x) d x

\int 3 cos^{2} (5 x) sin (5 x) cot (5 x) d x = \frac{3}{5} sin (5 x) - \frac{1}{5} sin^{3} (5 x)

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - (\frac{3}{5} sin (5 x) - \frac{1}{5} sin^{3} (5 x))

Vereinfache

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - \frac{3}{5} sin (5 x) + \frac{1}{5} sin^{3} (5 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - \frac{3}{5} sin (5 x) + \frac{1}{5} sin^{3} (5 x) + C

\int 2 e^{- 3 x} d x

x \to 0 lim (cos^{\frac{1}{x}} (x))

sin^{2} (y) d x + cos^{2} (x) d y = 0

x \to - 5 lim (2 x + 3)

in v erse l a pl a ce \frac{1 + e ^{- π s}}{s ^{2} + 1}