Evaluate : `intx^(2)sinxdx`.

1.	Evaluate : `intx^(2)sinxdx`.
Answer» Integrating by parts, taking `x^(2)` as the first function, we get `intx^(2)sinxdx=x^(2)intsinxdx-int[(d)/(dx)(x^(2))intsinxdx]dx` `=x^(2)(-cosx)-int2x(-cosx)dx` `=-x^(2)cosx+2intxcosxdx` `=-x^(2)cosx+2[x(sinx)-int{(d)/(dx)(x)intcosxdx}dx]` [integrating x cos x by parts] `=-x^(2)cosx+2[xsinx-intsinxdx]` `=-x^(2)cosx+2[xsinx+cosx]+C`.

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