What is the integral of tan(x)-2sin(x) ?

The integral of tan(x)-2sin(x) is -ln|cos(x)|+2cos(x)+C

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integral of tan(x)-2sin(x)

\int tan (x) - 2 sin (x) d x

- ln ∣ cos (x) ∣ + 2 cos (x) + C

Solution steps

\int tan (x) - 2 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 tan (x) d x - \int 2 sin (x) d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int 2 sin (x) d x = - 2 cos (x)

= - ln ∣ cos (x) ∣ - (- 2 cos (x))

Simplify

= - ln ∣ cos (x) ∣ + 2 cos (x)

Add a constant to the solution

= - ln ∣ cos (x) ∣ + 2 cos (x) + C

\frac{d}{d x} (\frac{300}{x})

\frac{\partial}{\partial x} (x yz)

f (x) g (x) h (x)

\int - \frac{1}{2} d x

What is the integral of tan(x)-2sin(x) ?
The integral of tan(x)-2sin(x) is -ln|cos(x)|+2cos(x)+C