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Question : 110 of 120
Marks:
+1,
-0
Solution:
Let
I=∫e−x‌cosec‌x(1+cot‌x)‌d‌x =∫e−x‌cosec‌d‌x+∫e−x‌cosec‌x⋅cot‌x‌d‌x
=cosec‌x⋅(−e−x)−∫(−cosec‌x⋅cot‌x)(−e−x)dx+∫e−x‌cosec‌x⋅cot‌x‌d‌x
=−e−x⋅cosec‌x−∫e−x⋅cosec‌x⋅cot‌d‌x+∫e−x‌cosec‌x⋅cot‌x‌d‌x
=−e−x⋅cosecx+c
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