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

\frac{\partial}{\partial x} (x^{4} + x^{2} y)

\int \frac{441 - x ^{2}}{x} d x

y = - x^{3} + 2 x^{2} + 1

\int \frac{e ^{3 x}}{1 + e ^{6 x}} d x

\frac{\partial}{\partial y} (y sin (x + y))

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