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

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

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

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

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

Solution steps

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

Expand

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

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

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 ( w )}{cos ( w )} d w - \int 4 cos (w) d w

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

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

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

Add a constant to the solution

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

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