Question

How do you integrate by substitution `int t^3sqrt(t^4+5)dt`?

Answer 1

`int t^3 sqrt(t^4+5) dt = 1/6(t^4+5)sqrt(t^4+5) + C`

Explanation:

Substitute:

`x = t^4+5`
`dx = 4t^3 dt`

so that the integral becomes:

`int t^3 sqrt(t^4+5) dt = 1/4 int sqrt(x)dx = 1/6xsqrt(x)+C = 1/6(t^4+5)sqrt(t^4+5) + C`