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

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

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integral of (4cos(x)+3x^3+2sin(x))

\int (4 cos (x) + 3 x^{3} + 2 sin (x)) d x

4 sin (x) + \frac{3 x ^{4}}{4} - 2 cos (x) + C

Solution steps

\int 4 cos (x) + 3 x^{3} + 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 4 cos (x) d x + \int 3 x^{3} d x + \int 2 sin (x) d x

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

\int 3 x^{3} d x = \frac{3 x ^{4}}{4}

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

= 4 sin (x) + \frac{3 x ^{4}}{4} - 2 cos (x)

Add a constant to the solution

= 4 sin (x) + \frac{3 x ^{4}}{4} - 2 cos (x) + C

\frac{d y}{d x} y^{3} = 5 x^{3} + 2 x

\frac{\partial}{\partial x} (9 + x^{2})

f (x) = 4 x^{2}, at x = 10

\frac{d}{d x} (1500 x + 3000 (2 x + 3)^{- 1} - 1000)

\frac{d}{d x} (y sin (x))

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