What is the integral of-4sin(2x)+3 ?

The integral of-4sin(2x)+3 is 2cos(2x)+3x+C

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integral of-4sin(2x)+3

\int - 4 sin (2 x) + 3 d x

2 cos (2 x) + 3 x + C

Solution steps

\int - 4 sin (2 x) + 3 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 4 sin (2 x) d x + \int 3 d x

\int 4 sin (2 x) d x = - 2 cos (2 x)

\int 3 d x = 3 x

= - (- 2 cos (2 x)) + 3 x

Simplify

= 2 cos (2 x) + 3 x

Add a constant to the solution

= 2 cos (2 x) + 3 x + C

\frac{d}{d x} (\frac{6 x - 1}{4 x + 5})

\int \frac{1}{2 x + 3} d x

\frac{d}{d x} ((\frac{1}{2} x^{2} - 3)^{2})

x^{2} \frac{d y}{d x} = (x + 1) y

y = x e^{- x}, y = 0, x = 4

What is the integral of-4sin(2x)+3 ?
The integral of-4sin(2x)+3 is 2cos(2x)+3x+C