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Beliebt Rechnen >

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

Lösung

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

Lösung

tan (x) + 2 ln tan (\frac{x}{2}) - x - cot (x) + C

Schritte zur Lösung

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

Multipliziere aus

(sec (x) + cot (x))^{2} : sec^{2} (x) + 2 sec (x) cot (x) + cot^{2} (x)

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int sec^{2} (x) + 2 sec (x) cot (x) - 1 + csc^{2} (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 sec^{2} (x) d x + \int 2 sec (x) cot (x) d x - \int 1 d x + \int csc^{2} (x) d x

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

\int 2 sec (x) cot (x) d x = 2 ln tan (\frac{x}{2})

\int 1 d x = x

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

= tan (x) + 2 ln tan (\frac{x}{2}) - x - cot (x)

Füge eine Konstante zur Lösung hinzu

= tan (x) + 2 ln tan (\frac{x}{2}) - x - cot (x) + C

Graph

Beliebte Beispiele

derivative of (6x^2+5(3x+sqrt(x)))

\frac{d}{d x} ((6 x^{2} + 5) (3 x + x))

derivative (x+2)/(x^2-4)

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

(d^2y)/(dx^2)=sin(2x)

\frac{d ^{2} y}{d x ^{2}} = sin (2 x)

integral from 1 to 2 of ((2sqrt(x-1)))/x

\int_{1}^{2} \frac{( 2 x - 1 )}{x} d x

inverselaplace 1/(s+4)

in v erse l a pl a ce \frac{1}{s + 4}