User:Deathanatos/Math Sandbox

$$\int_0^1 e^{2x} dx$$ Essentially integration by substitution...

Let: $$u = 2x$$ Then: $$\tfrac{du}{dx} = 2$$ Rearrange: $$\tfrac{du}{2} = dx$$

Now substitute u in: $$\int_0^1 e^u dx$$

Substitute dx out: $$\int_0^1 e^u \tfrac{1}{2} du$$

Move 1/2 out: $$\tfrac{1}{2} \int_0^1 e^u du$$ - now integrate:

$$\tfrac{1}{2} \cdot e^u + C \Big| _0^1$$

Put u back in: $$\frac{e^{2x}}{2} + C \Big| _0^1$$