What is the integral of 8e^{2x}+6x ?

The integral of 8e^{2x}+6x is 4e^{2x}+3x^2+C

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integral of 8e^{2x}+6x

\int 8 e^{2 x} + 6 x d x

4 e^{2 x} + 3 x^{2} + C

Solution steps

\int 8 e^{2 x} + 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 8 e^{2 x} d x + \int 6 x d x

\int 8 e^{2 x} d x = 4 e^{2 x}

\int 6 x d x = 3 x^{2}

= 4 e^{2 x} + 3 x^{2}

Add a constant to the solution

= 4 e^{2 x} + 3 x^{2} + C

\frac{\partial}{\partial x} (9 x arctan (\frac{x}{y}))

y = e^{- x} sin (π) x

x \to 1 lim ({3 f (x) - 2 h (x)})

x \to 0 lim (\frac{cos ( 3 x )}{x + 3})

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

What is the integral of 8e^{2x}+6x ?
The integral of 8e^{2x}+6x is 4e^{2x}+3x^2+C