antiderivative

[happyman]

hi, i was wondering how one would find the antiderivative of (4x+3)^7, could you please show the process of coming to your answer, Thanks

 

[tkhunny]

Simple Substitution: u = 4x+3

OR

Keep the Chain Rule in mind and just write it down without the substitution.

 

[happyman]

i dont understand how you can apply substituion or the chain rule when trying to find the ANTIDERIVATIVE

 

[pka]

i dont understand how you can apply substituion or the chain rule when trying to find the ANTIDERIVATIVE

This may sound odd to you, but the best to learn to do that is to practice many derivatives involving the chain rule. Do them slowly watching the ‘shape’ of the answer.

 

[happyman]

is there anyway someone would be kind enough to show me how to solve this i am quite lost.

 

[Deleted member 4993]

Your response tells me that you did not try TK's response with paper-and-pencil - you just stared at it....

Suppose you had:

\(\displaystyle \int(ax+b)^n dx\)

substitute

u = ax + b <<<<<<<<<<<<<<<<<<<<<<<<<<< this is where you apply substitution in ANTIDERIVATIVE

du = a dx

\(\displaystyle \int(ax+b)^n dx\)

\(\displaystyle = \, \int u^n \cdot \frac{1}{a} du\)

Now continue....