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

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

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integral of 3sin(x)+2x

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

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

Solution steps

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

\int 3 sin (x) d x = - 3 cos (x)

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

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

Add a constant to the solution

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

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