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Beliebt Rechnen >

integral of sec(x)-cos(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

sec (x) - cos (x) : sin (x) tan (x)

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{1 - cos ^{2} ( x )}{cos ( x )} d x

Multipliziere aus

\frac{1 - cos ^{2} ( x )}{cos ( x )} : \frac{1}{cos ( x )} - cos (x)

= \int \frac{1}{cos ( x )} - cos (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 \frac{1}{cos ( x )} d x - \int cos (x) d x

\int \frac{1}{cos ( x )} d x = ln ∣ tan (x) + sec (x) ∣

\int cos (x) d x = sin (x)

= ln ∣ tan (x) + sec (x) ∣ - sin (x)

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative 1/2 ln(x)

d er i v a t i v e \frac{1}{2} ln (x)

integral of xln(sqrt(11)x)

\int x ln (11 x) d x

limit as x approaches (3pi)/2 of sin(x)

x \to \frac{3 π}{2} lim (sin (x))

derivative f(y)=ln(5x^2-x+1)

d er i v a t i v e f (y) = ln (5 x^{2} - x + 1)

integral of v/(3-0.001v^2)

\int \frac{v}{3 - 0.001 v ^{2}} d v