What is the integral of 4e^{2x}+3 ?

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

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integral of 4e^{2x}+3

\int 4 e^{2 x} + 3 d x

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

Solution steps

\int 4 e^{2 x} + 3 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 4 e^{2 x} d x + \int 3 d x

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

\int 3 d x = 3 x

= 2 e^{2 x} + 3 x

Add a constant to the solution

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

\frac{\partial}{\partial x} (\frac{( x y )}{( x - y )})

x \to 0 lim (x + ln (x))

y^{^{''}} + 2 y^{^{'}} + y = 16 e - t

\frac{d}{d y} (y cos (x y))

n = 1 \sum \infty 5 \cdot 3^{n}