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

\frac{2}{x}

1 (t - 4)

x \to 0 + lim (sin^{x} (x))

x \to 1 lim (2 x^{2} + x - 1)

\int 3 e^{x} + 7 sec^{2} (x) d x

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