What is the integral of cosh(x)+5/(sin(x)) ?

The integral of cosh(x)+5/(sin(x)) is sinh(x)+5ln|tan(x/2)|+C

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integral of cosh(x)+5/(sin(x))

\int cosh (x) + \frac{5}{sin ( x )} d x

sinh (x) + 5 ln tan (\frac{x}{2}) + C

Solution steps

\int cosh (x) + \frac{5}{sin ( 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 cosh (x) d x + \int \frac{5}{sin ( x )} d x

\int cosh (x) d x = sinh (x)

\int \frac{5}{sin ( x )} d x = 5 ln tan (\frac{x}{2})

= sinh (x) + 5 ln tan (\frac{x}{2})

Add a constant to the solution

= sinh (x) + 5 ln tan (\frac{x}{2}) + C

y^{^{''}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = 0

\int 7 e^{7 x} d x

x \to 1 lim (x^{2} - 3 x + 6)

\int sin (x) sin (3 x) sin (5 x) d x

\frac{d}{d x} (\frac{2 x ^{5} - 27}{x ^{4}})

What is the integral of cosh(x)+5/(sin(x)) ?
The integral of cosh(x)+5/(sin(x)) is sinh(x)+5ln|tan(x/2)|+C