What is the integral of (3tan(x)-4cos^2(x))/(cos(x)) ?

The integral of (3tan(x)-4cos^2(x))/(cos(x)) is 3sec(x)-4sin(x)+C

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

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

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

Solution steps

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

Expand

\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

Apply the Sum Rule:

\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)

Add a constant to the solution

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

5 x^{2} (3 x^{2} - 1)^{2}

\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

What is the integral of (3tan(x)-4cos^2(x))/(cos(x)) ?
The integral of (3tan(x)-4cos^2(x))/(cos(x)) is 3sec(x)-4sin(x)+C