Question

How do you find the integral `int 3t^2(t^3+4)^5 dt` using substitution?

Answer 1

`1/6(t^3+4)^6+C.`

Explanation:

Take `t^3+4=x rArr 3t^2dt=dx`

`:. I=int(t^3+4)^5(3t^2)dt`

`=intx^5dx=x^6/6=1/6(t^3+4)^6+C.`