What is the integral of (e^x+sin(x)+x) ?

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

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integral of (e^x+sin(x)+x)

\int (e^{x} + sin (x) + x) d x

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

Solution steps

\int e^{x} + 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 e^{x} d x + \int sin (x) d x + \int x d x

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

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

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

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

Add a constant to the solution

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

x \to 0 lim (\frac{2 x}{x ^{2}})

x \to 0 lim (- cos (x))

\int 6 x - x^{2} d x

\frac{d}{d x} (3 x^{2} - 2 x - 8)

y d x + (x - 8) d y = 0, y (9) = 36

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