What is the integral of (9sin(x)+4sec(x))/(tan(x)) ?

The integral of (9sin(x)+4sec(x))/(tan(x)) is 9sin(x)+4ln|tan(x/2)|+C

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integral of (9sin(x)+4sec(x))/(tan(x))

\int \frac{9 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

9 sin (x) + 4 ln tan (\frac{x}{2}) + C

Solution steps

\int \frac{9 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

Expand

\frac{9 sin ( x ) + 4 sec ( x )}{tan ( x )} : \frac{9 sin ( x )}{tan ( x )} + \frac{4 sec ( x )}{tan ( x )}

= \int \frac{9 sin ( x )}{tan ( x )} + \frac{4 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{9 sin ( x )}{tan ( x )} d x + \int \frac{4 sec ( x )}{tan ( x )} d x

\int \frac{9 sin ( x )}{tan ( x )} d x = 9 sin (x)

\int \frac{4 sec ( x )}{tan ( x )} d x = 4 ln tan (\frac{x}{2})

= 9 sin (x) + 4 ln tan (\frac{x}{2})

Add a constant to the solution

= 9 sin (x) + 4 ln tan (\frac{x}{2}) + C

f (x) = \frac{6}{3 x + 1}

f (x) = 8 - 2 x

\int \frac{x ^{3}}{x ^{4} + 1} d x

\frac{\partial}{\partial y} (e^{4 x y})

n = 0 \sum \infty (\frac{e}{10})^{n}

What is the integral of (9sin(x)+4sec(x))/(tan(x)) ?
The integral of (9sin(x)+4sec(x))/(tan(x)) is 9sin(x)+4ln|tan(x/2)|+C