Question

Write a value of

\[\int x^2 \sin x^3 \text{ dx }\]

Answer 1

    Let I = ∫  x² sin x³ dx  

Let x³ = t 
⇒ ​3x²  dx = dt

\[\Rightarrow x^2 \text{ dx }= \frac{dt}{3}\]
\[ \therefore I = \frac{1}{3}\int \text{ sin  t  dt}\]
\[ = \frac{1}{3}\left[ - \cos\text{  t }\right] + C\]
\[ = - \frac{1}{3}\cos \text{ x}^3 + C \left( \because t = x^3 \right)\]