4.sin x sin (cos x)

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Solution

∫ sinx⋅sin( cosx ) dx (1)

Consider cosx=t .

Therefore,

cosx=t

Differentiating both sides,

−sinxdx=dt

By substituting sinxdx=dt in equation (1), we get:

∫ sinx⋅sin( cosx ) dx=− ∫ ( sint )dt =−[ −cost ]+C =cos( cosx )+C

Thus, the required integral is I=cos( cosx )+C .

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