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

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

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integral of 2cos(x)+2x

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

2 sin (x) + x^{2} + C

Solution steps

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

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

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

= 2 sin (x) + x^{2}

Add a constant to the solution

= 2 sin (x) + x^{2} + C

\int (x^{2} - \frac{1}{x}) d x

\int (x^{2} + 1) cos (3 x) d x

\int \frac{y}{1 + 3 y ^{2}} d y

\int 1 + x^{2} x^{3} d x

\int x^{2} arctan (x^{3}) d x

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