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Question
Integrate the following with respect to x :
sin5x cos3x
Solution
`int sin^5x cos^3x "d"x = int sin^5x cos^2x * cos x "d"x`
= `int sin^5x (1 - sin^2x) * cos x "d"x`
= `int (sin^5x - sin^7x) * cos x "d"x`
= `int sin^5x cos x "d'x - nt sin^7x cos x "d"x`
Put u = sin x
du = cos x dx
`int sin^5x cos^3x "d"x = int "u"^5 "du" - int"u"^7 "du"`
= `"u"^6/6 - "u"^8/8 + "c"`
`int sin^5x cos^3x "d"x = (sinx)^6/6 - (sinx)^8/8 + "c"`
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