What is the integral of 3+(x^2+2)e^{x^3+6x} ?

The integral of 3+(x^2+2)e^{x^3+6x} is 3x+1/3 e^{x^3+6x}+C

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integral of 3+(x^2+2)e^{x^3+6x}

\int 3 + (x^{2} + 2) e^{x^{3} + 6 x} d x

3 x + \frac{1}{3} e^{x^{3} + 6 x} + C

Solution steps

\int 3 + (x^{2} + 2) e^{x^{3} + 6 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 d x + \int (x^{2} + 2) e^{x^{3} + 6 x} d x

\int 3 d x = 3 x

\int (x^{2} + 2) e^{x^{3} + 6 x} d x = \frac{1}{3} e^{x^{3} + 6 x}

= 3 x + \frac{1}{3} e^{x^{3} + 6 x}

Add a constant to the solution

= 3 x + \frac{1}{3} e^{x^{3} + 6 x} + C

\int \frac{8}{6 + 2 x} d x

\frac{\partial}{\partial x} (x e^{- t} sin (θ))

x \to 1 lim (\frac{\frac{2}{x} - 2}{x - 1})

\frac{\partial}{\partial x} (e^{x} + e^{- x})

f (x) = x^{3} - 8 x + 2

What is the integral of 3+(x^2+2)e^{x^3+6x} ?
The integral of 3+(x^2+2)e^{x^3+6x} is 3x+1/3 e^{x^3+6x}+C