integral of (cot^4(x))/(csc^2(x))

Lösung

\int \frac{cot ^{4} ( x )}{csc ^{2} ( x )} d x

- cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

Schritte zur Lösung

\int \frac{cot ^{4} ( x )}{csc ^{2} ( x )} d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{cos ^{4} ( x )}{sin ^{2} ( x )} d x

Wende die partielle Integration an

= - cos^{4} (x) cot (x) - \int 4 cos^{3} (x) sin (x) cot (x) d x

\int 4 cos^{3} (x) sin (x) cot (x) d x = 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

= - cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

Füge eine Konstante zur Lösung hinzu

= - cos^{4} (x) cot (x) - 4 (cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))) + C

f (x) = 3 sin (2 x)

\frac{\partial}{\partial x} (4 x^{3} y + x y^{2})

d er i v a t i v e - \frac{2 x}{( 4 + x ^{2} ) ^{2}}

t an g e n t x^{3} - 6 x^{2} - 34 x + 40, at x = 4

\frac{\partial}{\partial z} (\frac{x y}{x + y + z})