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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  (sin⁡  x  −  cos⁡  x)4  (sin⁡  x  +  cos⁡  x)  dx\int \,\,{\left( {\sin \,\,x\,\, - \,\,\cos \,\,x} \right)^4}\,\,\left( {\sin \,\,x\,\, + \,\,\cos \,\,x} \right)\,\,dx is equal to
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Correct option: B
(sin⁡  x  −  cos⁡  x)55  +  c\frac{{{{\left( {\sin \,\,x\,\, - \,\,\cos \,\,x} \right)}^5}}}{5}\,\, + \,\,c
Option B ((sin⁡x,−,cos⁡x)55+,c\frac{{{{\left( {\sin \\ x\\, - \\,\cos \\ x} \right)}^5}}}{5}\\ + \\,c) is correct because the integral can be solved by direct substitution.

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