CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsIntegrals and it's Applications2 Marks
Question
Evaluate: $\int \frac{e^x(x-3)}{(x-1)^3} d x$
✓
Answer
$\int \frac{e^x(x-3)}{(x-1)^3} d x=\int e^x\left[\frac{(x-1)-2}{(x-1)^3}\right] d x$ $=\int e^x\left[\frac{1}{(x-1)^2}+\left(\frac{-2}{(x-1)^3}\right)\right] d x$ $\left(\because \int e^x\left[f(x)+f^{\prime}(x)\right] d x=e^x f(x)+c\right)$ $1=\frac{e^x}{(x-1)^2}+C$
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