The value of ∫1√x−12+√22dx is log∣∣∣x−2+√x−12+2∣∣∣ log∣

| The value of

\int \frac{1}{\sqrt{{(x - 1)}^{2} + {(\sqrt{2})}^{2}}} d x

A. $log ∣ ∣ ∣ x - 2 + \sqrt{{(x - 1)}^{2} + 2} ∣ ∣ ∣$

B. $log ∣ ∣ ∣ x - 2 + \sqrt{{(x - 2)}^{2} + 1} ∣ ∣ ∣$

C. $log ∣ ∣ ∣ x - 1 + \sqrt{{(x - 1)}^{2} + 2} ∣ ∣ ∣$

D. $log ∣ ∣ ∣ x - 2 + \sqrt{{(x - 1)}^{2} + 1} ∣ ∣ ∣$

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

We know that $\int \frac{1}{\sqrt{x^{2} + a^{2}}} d x = log ∣ ∣ x + \sqrt{x^{2} + a^{2}} ∣ ∣$
Here , instead of x we have x - 1 and the value of a will be = $\sqrt{2}$

So $\int \frac{1}{\sqrt{(x - 1)^{2} + (\sqrt{2})^{2}}} d x$ would be equal to $log | x - 1 + \sqrt{(x - 1)^{2} + 2} |$

The value of ∫1√x−12+√22dx is log∣∣∣x−2+√x−12+2∣∣∣ log∣

Right Answer is: C

SOLUTION

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