Question
Download Solution PDF\(\rm \int e^x \left(\dfrac{1}{x}- \dfrac{1}{x^2}\right)dx \) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
\(\rm \int e^x \left(f(x)+f'(x)\right)dx \) = ex f(x) + c
गणना:
माना कि \(\rm I=\int e^x \left(\dfrac{1}{x}- \dfrac{1}{x^2}\right)dx \) है।
माना कि f(x) = \(\rm 1\over x\) है।
⇒ \(\rm f'(x) = - {1\over x^2}\)
∴ \(\rm I=\int e^x \left(\dfrac{1}{x}- \dfrac{1}{x^2}\right)dx \)= \(\rm \int e^x \left(f(x)+f'(x)\right)dx \)
= ex f(x) + c
= \(\rm e^x ({1\over x})\) + c
अतः विकल्प (3) सही है।
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