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Beliebt Rechnen >

integral of (cos(x)-tan(x))/(cos^2(x))

Lösung

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

Lösung

ln ∣ tan (x) + sec (x) ∣ - \frac{tan ^{2} ( x )}{2} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= ln ∣ tan (x) + sec (x) ∣ - \frac{tan ^{2} ( x )}{2}

Füge eine Konstante zur Lösung hinzu

= ln ∣ tan (x) + sec (x) ∣ - \frac{tan ^{2} ( x )}{2} + C

Graph

Beliebte Beispiele

derivative sqrt(4x)

d er i v a t i v e 4 x

derivative of sin(x+4x^2)

\frac{d}{d x} (sin (x) + 4 x^{2})

sum from n=2 to infinity of 1/(2ie^nn^2)

n = 2 \sum \infty \frac{1}{2 i e ^{n} n ^{2}}

integral of 1/(e^{a*x)}

\int \frac{1}{e ^{a \cdot x}} d x

derivative f(x)=\sqrt[3]{x^2}+sqrt(x)

d er i v a t i v e f (x) = 3 x^{2} + x