What is the integral of (5cos^2(x)-3tan(x))/(cos(x)) ?

The integral of (5cos^2(x)-3tan(x))/(cos(x)) is 5sin(x)-3sec(x)+C

Popular >

integral of (5cos^2(x)-3tan(x))/(cos(x))

\int \frac{5 cos ^{2} ( x ) - 3 tan ( x )}{cos ( x )} d x

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

Solution steps

\int \frac{5 cos ^{2} ( x ) - 3 tan ( x )}{cos ( x )} d x

Expand

\frac{5 cos ^{2} ( x ) - 3 tan ( x )}{cos ( x )} : 5 cos (x) - \frac{3 tan ( x )}{cos ( x )}

= \int 5 cos (x) - \frac{3 tan ( x )}{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 5 cos (x) d x - \int \frac{3 tan ( x )}{cos ( x )} d x

\int 5 cos (x) d x = 5 sin (x)

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

= 5 sin (x) - 3 sec (x)

Add a constant to the solution

= 5 sin (x) - 3 sec (x) + C

\frac{d}{d x} (cosh (e^{x}))

\frac{d y}{d x} + 3 y = 70

\int_{1}^{\infty} \frac{8}{x ^{2} + 1} d x

\int (csc^{2} (x) - 2 e^{x}) d x

x \to 2 lim (x^{3} + 4 x^{2} - 2 x + 2)

What is the integral of (5cos^2(x)-3tan(x))/(cos(x)) ?
The integral of (5cos^2(x)-3tan(x))/(cos(x)) is 5sin(x)-3sec(x)+C