Evaluate the following integrals: 1) integral cos(2x)dx 2) integral e^(2x-4)dx 3) integral e^(3x)dx

Let $u = 2x$.
Then, differentiate $u$ with respect to $x$:

$$\frac{du}{dx} = 2$$ $$du = 2\,dx$$ $$dx = \frac{1}{2}\,du$$

The integral of $\cos(u)$ is $\sin(u)$.

$$\frac{1}{2} \sin(u) + C$$

$$\boxed{\frac{1}{2} \sin(2x) + C}$$

2) Evaluate $\int e^{2x-4}\,dx$.

Let $u = 2x-4$.
Then, differentiate $u$ with respect to $x$:

$$\frac{du}{dx} = 2$$ $$du = 2\,dx$$ $$dx = \frac{1}{2}\,du$$

The integral of $e^u$ is $e^u$.

$$\frac{1}{2} e^{u} + C$$

$$\boxed{\frac{1}{2} e^{2x-4} + C}$$

3) Evaluate $\int e^{3x}\,dx$.

Let $u = 3x$.
Then, differentiate $u$ with respect to $x$:

$$\frac{du}{dx} = 3$$ $$du = 3\,dx$$ $$dx = \frac{1}{3}\,du$$

The integral of $e^u$ is $e^u$.

$$\frac{1}{3} e^{u} + C$$

$$\boxed{\frac{1}{3} e^{3x} + C}$$

4) Evaluate $\int (2x+3)^{1/2}\,dx$.

Let $u = 2x+3$.
Then, differentiate $u$ with respect to $x$:

$$\frac{du}{dx} = 2$$ $$du = 2\,dx$$ $$dx = \frac{1}{2}\,du$$