Question:
Evaluate the following integrals:
$\int x^{3} \cos x^{4} d x$
Solution:
Assume $x^{4}=t$
$d\left(x^{4}\right)=d t$
$4 x^{3} d x=d t$
$x^{3} d x=\frac{d t}{4}$
Substituting $t$ and $d t$
$\Rightarrow \int \frac{1}{4} \cos t d t$
$\Rightarrow \frac{1 \sin t}{4}+c$
But $t=x^{4}$
$\Rightarrow \frac{1}{4} \sin x^{4}+c$