Question

\[\int x^3 \cos x^4 dx\]

Answer 1

\[\int x^3 \cdot \cos \left( x^4 \right) dx\]
\[\text{Let x}^4 = t\]
\[ \Rightarrow 4 x^3 dx = dt\]
\[ \Rightarrow x^3 dx = \frac{dt}{4}\]
\[Now, \int x^3 \cdot \cos \left( x^4 \right) dx\]
\[ = \frac{1}{4}\int\cos \left( t \right) dt\]
\[ = \frac{1}{4}\left[ \text{sin} \left( t \right) \right] + C\]
\[ = \frac{1}{4}\left[ \text{sin x}^4 \right] + C\]