Mathematics

$$\displaystyle\int { \sin { x\sin { \left( \cos { x }  \right)  }  }  } dx$$


SOLUTION
$$I=\int { \sin { x } \sin { (\cos { x } ) } dx } $$
Putting $$\cos { x } =t$$
differentiating both sides, 
$$-\sin { x } dx=dt$$
and substituting the values, 
$$I=-\int { \sin { t } dt } =-(-\cos { t } )=\cos { t } $$
$$ =\cos { (\cos { x } ) } \quad [\therefore \cos { x } =t]$$
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