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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy
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Application +4 | -1
If an anti-derivate of f  (x)f\,\,\left( x \right) is e^x and that of g  (x)\mathrm{g}\,\,\left( x \right) is cos⁡x, then ∫  f(x)  cos⁡  x  dx  +  ∫  g  (x)  ex dx\int \,\,f\left( x \right)\,\,\cos \,\,x\,\,dx\,\, + \,\,\int \,\,\mathrm{g}\,\,\left( x \right)\,\,{e^x}\,dx is equal to
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Correct option: C
ex  cos⁡  x  +  c{e^x}\,\,\cos \,\,x\,\, + \,\,c
Option C (ex  cos⁡  x  +  c{e^x}\,\,\cos \,\,x\,\, + \,\,c) is correct because integrating by parts and simplifying leads to this result.

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