Question

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

Answer 1

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