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

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

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integral of 2sin(x)+x

\int 2 sin (x) + x d x

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

Solution steps

\int 2 sin (x) + 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 2 sin (x) d x + \int x d x

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (5 x + \frac{3}{x})

x \to 0 lim (sin (x) ln (3 x))

(\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x))^{^{'}}

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

cos (x) y^{^{'}} + sin (x) y = 1

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