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Beliebt Rechnen >

integral of (xsin(x))/((cos(x))^2)

Lösung

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

Lösung

x sec (x) - ln ∣ tan (x) + sec (x) ∣ + C

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int x sec (x) tan (x) d x

Wende die partielle Integration an

= x sec (x) - \int sec (x) d x

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= x sec (x) - ln ∣ tan (x) + sec (x) ∣

Füge eine Konstante zur Lösung hinzu

= x sec (x) - ln ∣ tan (x) + sec (x) ∣ + C

Graph

Beliebte Beispiele

derivative of x^2y^4

\frac{d}{d x} (x^{2} y^{4})

limit as x approaches 2 of x^2-5

x \to 2 lim (x^{2} - 5)

limit as x approaches 0 of (1-e^{-x})/x

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

derivative of (x^2/(x^3))

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

derivative e^x(x^2+1)(x+4)

d er i v a t i v e e^{x} (x^{2} + 1) (x + 4)