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int(sin(101x).sin^(99)x)dx equals...

`int(sin(101x).sin^(99)x)dx` equals

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`I=intsin(100x+x)sin^(99)xdx`
`=int sin100x cosx sin^(99)xdx+int sinx cos100x sin^(99) x dx`
`=int sin100x cosx sin^(99)xdx+int cos100x .sin^(100) x dx`
`=int sin100x. cosx sin^(99)xdx+sin^(100) x .(sin 100x)/(100) -int (100sin^(99)xcosx.sin 100x)/(100)dx`
`=(sin^(100)x sin 100x)/(100)+c`
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