A) \[\frac{\sin x-\cos x}{5}+c\]
B) \[\frac{{{(\sin x-\cos x)}^{5}}}{5}+c\]
C) \[\frac{{{(\sin x-\cos x)}^{4}}}{4}+c\]
D) \[\frac{{{(\sin x+\cos x)}^{5}}}{5}+c\]
E) None of the above
Correct Answer: B
Solution :
Let\[I=\int{{{(\sin x-\cos x)}^{4}}}(\sin x+\cos x)dx\] Put \[sin\text{ }x-cos\text{ }x=t\] \[\Rightarrow \]\[(\cos x+\sin x)dx=dt\] \[\therefore \]\[I=\int{{{t}^{4}}dt}=\frac{{{t}^{5}}}{5}+c\] \[=\frac{{{(\sin x-\cos x)}^{5}}}{5}+c\]
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