Could you please help me find this integral?

Question

Find the integral. Assume m ≠ 0. Use c for the constant of integration

∫ (mx+b)⁵ dx

There was a problem like this in my book so I followed the steps but it marked me wrong.

I got (mx+b)⁶/6 +C

What did I do wrong?

Answer 1

You know that (mx+b) is a linear factor, where m and b are constants.

 

Let                  u = mx + b

                     du = mdx

             (1/m)du = dx

 

Substituting,

 

(1/m)∫u⁵du =

 

(1/m)(1/6)u⁶ =

 

(1 / (6m))(mx + b)⁶ + C

 

 

Answer 2

You forgot the chain rule  

 

Test your answer

 

The derivative of your answer would have an extra multiple of m

 

Therefore the correct answer is (mx+b)^6/(6m) + C