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Question
Integrate the following functions w.r.t. x : sin4x.cos3x
Solution
Let I = `int sin^4x.cos^3x dx`
= `int sin^4x.cos^2x.cos x dx`
= `int sin^4x (1 - sin^2x) cos x dx`
Put sin x = t
∴ cos x dx = dt
∴ I = `int t^4(1 - t^2)dt`
= `int (t^4 - t^6)dt`
= `int t^4 dt - int t^6 dt`
= `t^5/(5) - t^7/(7) + c`
= `(1)/(5)sin^5x - (1)/(7)sin^7 x + c`.
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