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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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The integral of f(x)=3xcos⁡xf(x)=3^x \cos x is given by
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Correct option: C
3x(sin⁡x+cos⁡log⁡3)(1+(log⁡3)2)\frac{3^x(\sin x+\cos \log 3)}{\left(1+(\log 3)^2\right)}
Option D is correct because the integral of 3xcos⁡x3^x \cos x is 3x(log⁡3sin⁡x+cos⁡x)(1+(log⁡3)2)+C\frac{3^x(\log 3 \sin x+\cos x)}{\left(1+(\log 3)^2\right)}+C after integrating by parts twice.

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