What is the integral of ((7sin(x)+4sec(x)))/(tan(x)) ?

The integral of ((7sin(x)+4sec(x)))/(tan(x)) is 7sin(x)+4ln|tan(x/2)|+C

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integral of ((7sin(x)+4sec(x)))/(tan(x))

\int \frac{( 7 sin ( x ) + 4 sec ( x ) )}{tan ( x )} d x

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

Solution steps

\int \frac{7 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

Expand

\frac{7 sin ( x ) + 4 sec ( x )}{tan ( x )} : \frac{7 sin ( x )}{tan ( x )} + \frac{4 sec ( x )}{tan ( x )}

= \int \frac{7 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{7 sin ( x )}{tan ( x )} d x + \int \frac{4 sec ( x )}{tan ( x )} d x

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

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

= 7 sin (x) + 4 ln tan (\frac{x}{2})

Add a constant to the solution

= 7 sin (x) + 4 ln tan (\frac{x}{2}) + C

f (x) = 200 + \frac{7}{x} + \frac{x ^{2}}{7}

y^{^{'}} = x (9 - y)

n = 1 \sum \infty \frac{1}{n + 9}

\int \frac{( x - 4 ) ^{2} ( x + 1 )}{x} d x

x y^{^{'}} = 2 y + 8 x

What is the integral of ((7sin(x)+4sec(x)))/(tan(x)) ?
The integral of ((7sin(x)+4sec(x)))/(tan(x)) is 7sin(x)+4ln|tan(x/2)|+C