integral of cos^3(3θ)sin^{-2}(3θ)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e \frac{2 t + 1}{t + 3}

d er i v a t i v e 8 x + 9 x e^{x}

\int cos (\frac{nπ x}{L}) d x

\frac{d}{d x} (3^{2 x^{2}} \cdot x)

\frac{d}{d x} (\frac{10}{x ^{2} + 1})