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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= sec (x) - ln ∣ tan (x) + sec (x) ∣

Füge eine Konstante zur Lösung hinzu

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

\int x^{2} e^{3 x^{3} - 1} d x

\int \frac{3 x ^{3}}{x - 2} d x

\int x (14 x^{2} + x) d x

\int 10 (3 x + 4)^{2} d x

\int 3 x^{5} d x