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

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

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

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

- 2 cos (x) + ln ∣ cos (x) ∣ + C

Solution steps

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

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

\int tan (x) d x = - ln ∣ cos (x) ∣

= - 2 cos (x) - (- ln ∣ cos (x) ∣)

Simplify

= - 2 cos (x) + ln ∣ cos (x) ∣

Add a constant to the solution

= - 2 cos (x) + ln ∣ cos (x) ∣ + C

\frac{\partial}{\partial x} (sin (π (4 x - y)))

\frac{d p}{2 ( p + 3 )} = \frac{d v}{- v}

x \to 0 + lim (x sin (x))

\int x^{2} x e^{x^{2}} d x

y^{3} - (14 x + 2) + 3 x y^{2} y^{^{'}} = 0

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