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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int e^x \large\frac{(x+6)}{(x+7)^2}$$dx$

$(a)\;e^x (x+7)+c \\(b)\; (x+7)^2+c \\(c)\; e^x (\frac{1}{x+7})+c \\ (d)\;e^x (x+7)^2+c$

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A)
$\int \large\frac{e^x}{(x+7)} - \int \large\frac{e^x}{(x+7)^2} $$dx$
$\int e^x [f'(x)+f(x)]dx=e^x . f(x) +c$
=>$ e^x (\large\frac{1}{x+7})$$+c$
Hence c is the correct answer.
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