integral of (3tan(x)-4cos^2(x))/(cos(x))

Lösung

\int \frac{3 tan ( x ) - 4 cos ^{2} ( x )}{cos ( x )} d x

3 sec (x) - 4 sin (x) + C

Schritte zur Lösung

\int \frac{3 tan ( x ) - 4 cos ^{2} ( x )}{cos ( x )} d x

Multipliziere aus

\frac{3 tan ( x ) - 4 cos ^{2} ( x )}{cos ( x )} : \frac{3 tan ( x )}{cos ( x )} - 4 cos (x)

= \int \frac{3 tan ( x )}{cos ( x )} - 4 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{3 tan ( x )}{cos ( x )} d x - \int 4 cos (x) d x

\int \frac{3 tan ( x )}{cos ( x )} d x = 3 sec (x)

\int 4 cos (x) d x = 4 sin (x)

= 3 sec (x) - 4 sin (x)

Füge eine Konstante zur Lösung hinzu

= 3 sec (x) - 4 sin (x) + C

\int ((x - 1)^{5} + 3 (x - 1)^{2} + 5) d x

\frac{\partial}{\partial x} (e^{x} (sin (y) - y))

x \to + 1 + lim (2 x - 2 - 2)

\int \frac{1}{x - 7} d x

\int \frac{6 x - 5}{3 x ^{2} + 5} d x