The correct option is B e^x.2√(x 1)+c ∫ e^x(2x 1√(x 1))dx =∫ e^x(2x 2+1√(x 1))dx=∫ e^x(2√(x 1)+1√(x 1))dx It is in the form of ∫ e^x[f(x)+f^ ...

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Special Integrals - 1

∫ ex2x-1/√x-1...

Question

$\int e^{x} \frac{2 x - 1}{\sqrt{x - 1}} d x =$

e^{x} .2 \sqrt{x + 1} + c

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e^{x} .2 \sqrt{x - 1} + c

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e^{x} . \sqrt{x - 1} + c

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e^{x} . (x - 1) + c

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Solution

The correct option is B $e^{x} .2 \sqrt{x - 1} + c$
$\int e^{x} (\frac{2 x - 1}{\sqrt{x - 1}}) d x$
$= \int e^{x} (\frac{2 x - 2 + 1}{\sqrt{x - 1}}) d x = \int e^{x} (2 \sqrt{x - 1} + \frac{1}{\sqrt{x - 1}}) d x$
It is in the form of
$\int e^{x} [f (x) + f^{1} (x)] d x = e^{x} f (x) + c$
Hence the value of integral is
$= e^{x} 2 \sqrt{x - 1} + c$

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