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Integrate following w.r.t.x, sin^(5)xcos...

Integrate following w.r.t.x, `sin^(5)xcos^(4)xdx`.

Text Solution

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Consider `I=intsin^(5)xcos^(4)xdx` ltbr. `I=int(1-cos^(2)x)^(2)cos^(4)x*sinxdx`,
Put `cosx=t`, as `m=5` (odd)
`-sinxdx=dt`
`:.l=-int(1-t^(2))^(2)t^(4)dtimpliesl=-int(t^(4)-2t^(6)+t^(8))dt`
`:.l=-(1)/(9)cos^(9)x+(2)/(7)cos^(7)x-(1)/(5)cos^(5)x+C`
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