Question

Evaluate the integral using integration by parts with the indicated choices of u and dv. (use c for the constant of integration.) 7x2 ln(x) dx; u = ln(x), dv = 7x2 dx

Answer 1

(7/3) x^3 ln x - (7/9) x^3 + c.

Explanation:

∫udv = uv - ∫vdu

u = ln x and dv = 7x^2dx so,

du = 1/x and v = 7x^3/3 so:

∫7x^2 ln x = (7x^3/3) ln x - 7 ∫x^3/3 * 1/x dx

= 7/3 x^3 ln x - 7 ∫x^2/3 dx

= 7/3 x^3 ln x - 7/x^3/2 * 1/3 dx

= 7/3 x^3 ln x - 7/9 x^3 + c.