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Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]3 Marks
Question
Evaluate $\int e ^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x$
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Answer

Let $I =\int e ^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x$
Put $f ( x )=\frac{1}{x}$
$ \therefore f ^{\prime}( x )=-\frac{1}{x^2}$
$\therefore I =\int e ^x\left[ f (x)+ f ^{\prime}(x)\right] d x$
$= e ^x \cdot f (x)+ c$
$\therefore I = e ^x \cdot \frac{1}{x}+ c $

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