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

The integral of 4x+sin(3x) is 2x^2-1/3 cos(3x)+C

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integral of 4x+sin(3x)

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

2 x^{2} - \frac{1}{3} cos (3 x) + C

Solution steps

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

\int 4 x d x = 2 x^{2}

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

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

Add a constant to the solution

= 2 x^{2} - \frac{1}{3} cos (3 x) + C

(6.4) (2.1)

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

y = 1.00059 e^{(2.39736)} - 1.0005

\frac{d}{d x} (\frac{1}{2 x + 7})

f (x) = x \cdot e^{2 x - 4}

What is the integral of 4x+sin(3x) ?
The integral of 4x+sin(3x) is 2x^2-1/3 cos(3x)+C