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 " . `
\[ = x^2 \int\cos x dx - \int\left( \frac{d}{dx} x^2 \int\text{ cos x dx } \right)dx\]
\[ = x^2 \sin x - \int2x \text{ sin x dx }\]
\[ = x^2 \sin x - 2\left[ x\int\sin x - \int\left\{ \frac{d}{dx}\left( x \right)\int\text{ sin x dx } \right\}dx \right]\]
\[ = x^2 \sin x - 2\left[ - x\cos x + \int\text{ cos x dx } \right]\]
\[ = x^2 \sin x + 2x \cos x - 2 \sin x + C\]