U-substitution and integrals

Question

Evaluate the integral

∫(2x+4)(x2+4x+6)^5

by making the substitution u=x2+4x+6u=x2+4x+6.

Answer 1

integral of (2x+4)(x^2+4x+6)^5

= integral of u^5 du

= u^6/6 + C

= (1/6)(x^2+4x +6)^6 + C