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

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

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integral of 2x+sin(x)+C

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

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

Solution steps

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

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

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

\int C d x = C x

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

Add a constant to the solution

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

\int \frac{3}{( x + 1 ) ( x - 2 )} d x

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

\int (2 x + 3) \cdot (x^{2} + 3 x)^{5} d x

\int \frac{5 x ^{4}}{( 7 + x ^{5} ) ^{4}} d x

\int \frac{x}{( cos ( x ) ) ^{2}} d x

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