Question

How do you find the integral `int(5x+4)^4dx` using substitution?

Answer 1

`=1/25(5x+4)^5+C`

Explanation:

By substitution

`int(5x+4)^4dx`

`u=5x+1=>du=5dx=>dx=(du)/5`

`int(5x+4)^4dx=intu^4*(du)/5=dx`

`=1/5intu^4du=1/5xx1/5u^5+C`

`=1/25u^5+C=1/25(5x+4)^5+C`