Hi, i'm trying to solve this integral on this site : http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx. The first question of Example 2: sin(1-x)(2-cos(1-x))^4 dx and i substituted u=2-cos(1-x). So i solved for du= sin(1-x)dx but the author of the tutorial says it is du=-sin(1-x)dx. Since the derivative of cosx is -sinx then the two negatives become positive. Need some explanation why he still mainstains the negative infront of the sin. thanks

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Hi, i'm trying to solve this integral on this site : http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx. The first question of Example 2: sin(1-x)(2-cos(1-x))^4 dx and i substituted u=2-cos(1-x). So i solved for du= sin(1-x)dx but the author of the tutorial says it is du=-sin(1-x)dx. Since the derivative of cosx is -sinx then the two negatives become positive. Need some explanation why he still mainstains the negative infront of the sin. thanks

Mathematics
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when u take the derivative of 2-cos(1-x)= -(-sin)(1-x)(-1) derivative of the inside too derivative of (1-x)
that's because the negative come from differentiate of ( 1- x ) that is -1
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