Question

Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.) xe9x dx; u

Answer 1

Answer:

The answer is "$\bold{ \frac{ x \ e^{2x}}{2} - \frac{e^{2x}}{4}+C}$"

Step-by-step explanation:

Taking the integral $\int x^{2x} \ dx$  

Evaluating the integral by using integration:

$u=x\\\\dv=e^{2x} \ dx$

Let

$u=x\\\\ dv=e^{2x} dx$

Then,

$\to \frac{du}{dx}= 1 and v =\int e^{2X} \ dx \\\\\to du = 1 dx \\\\\to v = \frac{e^{2x}}{2}\\\\\text{integrate the above value}:\\\\\int u dv = uv - \int v du \\\\Now, \\\\\to \int x e^{2X} \ dx = x \frac{e^{2x}}{2} - \int \frac{e^{2x}}{2} dx$

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