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

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

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

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

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

Solution steps

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

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

\int 3 x^{2} d x = x^{3}

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

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

Add a constant to the solution

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

4 y^{^{''}} - 12 y^{^{'}} + 9 y = 0

\int e^{\frac{t}{RC}} d t

\int 9 x^{7} d x

n = 2 \sum \infty \frac{( - 1 ^{n} )}{n}

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