A) \[{{e}^{ln\,\,x}}(\sin \,\,x-\cos \,\,x)+c\]
B) \[(\sin \,\,x-x\,\,\cos \,\,x)+c\]
C) \[(x\,\,\sin \,\,x+\cos \,\,x)+c\]
D) \[(\sin \,\,x+x\,\,\cos \,\,x)-c\] Where ?c? is a constant of integration.
Correct Answer: B
Solution :
[b] Let \[I=\int{{{e}^{In\,x}}\sin x\,\,dx=\int{x\sin x\,\,dx(\because {{e}^{\log \,a}}=a)}}\] \[=-x\cos x+\int{1.\cos \,\,x\,\,dx=(\sin \,\,x-x\,\,\cos \,\,x)+c}\]
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