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

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

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

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

3 sec (β) - 4 sin (β) + C

Solution steps

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

Expand

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

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

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

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

\int 4 cos (β) d β = 4 sin (β)

= 3 sec (β) - 4 sin (β)

Add a constant to the solution

= 3 sec (β) - 4 sin (β) + C

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