integral of (cot^2(x)+cot^4(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cot^{2} (x) d x + \int cot^{4} (x) d x

\int cot^{2} (x) d x = - x - cot (x)

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (ln (\frac{x + 2}{x - 2}))

t an g e n t f (x) = 5 x, at x = 5

\int tan (5 x) sec^{2} (5 x) d x

a re a x - 2, x, [0, 4]

d er i v a t i v e [x + (x + sin^{2} (x))^{7}]^{5}