Question

Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.) xe7x dx; u

Answer 1

Answer:

$\frac{xe^{7x}}{7} + \frac{e^{7x}}{49}$

Step-by-step explanation:

Given the integral equation

$\int\limits{xe^{7x}} \, dx$

According to integration by part;

$\int\limits {u} \, dv = uv + \int\limits {v} \, du$

u = x, dv = e^7x

du/dx = 1

du = dx

$v = \int\limits {e^{7x}} \, dx \\v = e^7x/7$

Substitute the given values into the formula;

$\int\limits {xe^{7x}} \, dx = x(e^{7x}/7) + \int\limits ({e^{7x}/7}) \, dx\\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{7*7} \\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{49}$