Answer
\[ -\dfrac{1}{16}(-4t+1)^4+C\]
Work Step by Step
In order to integrate this function, we have to use an «u» substitution.
Choose an u, derivate it:
$ u=-4t+1$
$ du = -4 dt$
$ -\dfrac{1}{4}du=dx$
Then and substitute:
\[ -\dfrac{1}{4} \int u^3 du \]
Then integrate
\[ = -\dfrac{1}{16}u^4+C \]
And undo the substitution:
\[ -\dfrac{1}{16}(-4t+1)^4+C\]
