Determine the integral (Differentiation)?

Question

This is a tricky one. As it says determine the integral

6(3x+5)^11 dx

Answer 1

Let u = 3x + 5.  Then, du = 3 dx, so:

Integral[6(3x + 5)^11 dx] = Integral[2u^11 du] = (u^12)/6 + C = [(3x + 5)^12]/6 + C

Answer 2

You are going to use u-substitution here.

6(3x+5)^11 dx ,    set u= (3x+5) and therefore du=3dx  => dx=du/3

6u^11 * du/3 = 2u^11 du

Taking the integral, we get (1/6)u^12

= (1/6)(3x+5)^12

Hope that helps! Good luck! :-)