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

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

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

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

3 sec (θ) - 4 sin (θ) + C

Solution steps

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

Expand

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

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

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

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

\int 4 cos (θ) d θ = 4 sin (θ)

= 3 sec (θ) - 4 sin (θ)

Add a constant to the solution

= 3 sec (θ) - 4 sin (θ) + C

x \to 0 + lim (\frac{ln ^{2} ( x )}{2})

\frac{\partial}{\partial y} (x^{2} + \frac{x}{y})

\int x^{11} x^{6} + 6 d x

2 x^{2} - 3 x + 4

x \to 1 lim (\frac{x - 2}{x - 1})

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