Question

\[\int x^2 \text{ cos x dx }\]

Answer 1

\[\int x^2 \text{ cos x dx }\]
`  " Taking x"^2" as the first function and  cos x as the second function . " `
\[ = x^2 \int\text{ cos x dx } - \int\left\{ \frac{d}{dx}\left( x^2 \right)\int\text{ cos x dx }\right\}dx\]
\[ = x^2 \sin x - \int2x \text{ sin x dx }\]
\[ = x^2 \sin x - 2\left[ x\int\sin x - \int\left\{ \frac{d}{dx}\left( x \right)\int\text{ sin x dx }\right\}dx \right]\]
\[ = x^2 \sin x + 2x\cos x - 2\int\text{ cos x dx }\]
\[ = x^2 \sin x + 2x \cos x - 2 \sin x + C\]