What is the integral of 2(e^{2t}+2) ?

The integral of 2(e^{2t}+2) is e^{2t}+4t+C

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integral of 2(e^{2t}+2)

\int 2 (e^{2 t} + 2) d t

e^{2 t} + 4 t + C

Solution steps

\int 2 (e^{2 t} + 2) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int e^{2 t} + 2 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int e^{2 t} d t + \int 2 d t)

\int e^{2 t} d t = \frac{1}{2} e^{2 t}

\int 2 d t = 2 t

= 2 (\frac{1}{2} e^{2 t} + 2 t)

Simplify

2 (\frac{1}{2} e^{2 t} + 2 t) : e^{2 t} + 4 t

= e^{2 t} + 4 t

Add a constant to the solution

= e^{2 t} + 4 t + C

y^{^{'}} + \frac{1}{3} y = e^{x} y^{4}

\frac{\partial}{\partial x} (7 cos (y e^{x y}) sin (x))

sin (t) \cdot sin (3 t)

\int x sin^{2} (4 x) d x

y = ∣ x - 3 ∣, y = \frac{x}{2}, y = 0

What is the integral of 2(e^{2t}+2) ?
The integral of 2(e^{2t}+2) is e^{2t}+4t+C