What is the integral of 2cos(-4x)+1 ?

The integral of 2cos(-4x)+1 is x+1/2 sin(4x)+C

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integral of 2cos(-4x)+1

\int 2 cos (- 4 x) + 1 d x

x + \frac{1}{2} sin (4 x) + C

Solution steps

\int 2 cos (- 4 x) + 1 d x

Simplify

2 cos (- 4 x) + 1 : 1 + 2 cos (4 x)

= \int 1 + 2 cos (4 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 1 d x + \int 2 cos (4 x) d x

\int 1 d x = x

\int 2 cos (4 x) d x = \frac{1}{2} sin (4 x)

= x + \frac{1}{2} sin (4 x)

Add a constant to the solution

= x + \frac{1}{2} sin (4 x) + C

\frac{\partial}{\partial x} (x^{2} - 4 x y + 3 y^{2})

\frac{d}{d x} ((x^{3} + 4) e^{x})

(s^{- \frac{1}{2}} + 2 s) (7 - s^{- 1})

f (x) = \frac{6}{5 x + 3}

\int_{0}^{2 π} e^{i x} d x

What is the integral of 2cos(-4x)+1 ?
The integral of 2cos(-4x)+1 is x+1/2 sin(4x)+C