What is the integral of (7sin(x)+2sec(x))/(tan(x)) ?

The integral of (7sin(x)+2sec(x))/(tan(x)) is 7sin(x)+2ln|tan(x/2)|+C

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integral of (7sin(x)+2sec(x))/(tan(x))

\int \frac{7 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

7 sin (x) + 2 ln tan (\frac{x}{2}) + C

Solution steps

\int \frac{7 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

Expand

\frac{7 sin ( x ) + 2 sec ( x )}{tan ( x )} : \frac{7 sin ( x )}{tan ( x )} + \frac{2 sec ( x )}{tan ( x )}

= \int \frac{7 sin ( x )}{tan ( x )} + \frac{2 sec ( x )}{tan ( 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{7 sin ( x )}{tan ( x )} d x + \int \frac{2 sec ( x )}{tan ( x )} d x

\int \frac{7 sin ( x )}{tan ( x )} d x = 7 sin (x)

\int \frac{2 sec ( x )}{tan ( x )} d x = 2 ln tan (\frac{x}{2})

= 7 sin (x) + 2 ln tan (\frac{x}{2})

Add a constant to the solution

= 7 sin (x) + 2 ln tan (\frac{x}{2}) + C

f^{^{'}} (x) = 22 x + ln (22 x)

\frac{s}{2 s + 4}

\frac{\partial}{\partial x} (\frac{5}{x y} + \frac{x}{y} + \frac{y}{x})

\frac{\partial}{\partial x} (8 + x ln (x y - 7))

\frac{d}{d x} (3^{\frac{x}{2}})

What is the integral of (7sin(x)+2sec(x))/(tan(x)) ?
The integral of (7sin(x)+2sec(x))/(tan(x)) is 7sin(x)+2ln|tan(x/2)|+C