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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
Integrate the function $e^x (\sin x + \cos x)$
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Answer

$I=\int e^{x}(\sin x+\cos x) d x$
Now,
Let sin x = f(x) $\Rightarrow$ f'(x) = cos x
We know that,
$\int e^{x}\left\{f(x)+f^{\prime}(x)\right\} d x=e^{x} f(x)+c$
Thus,
$\int e^{x}(\sin x+\cos x) d x=e^{x} \sin x+C$

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