We have, #10; #10; ∫1√(( 2 x^2)+1)dx #10; #10;Now, #10; #10; ∫1√(( 2 x^2 #10;)+1^2)dx #10; #10;Using ∫1√(x^2+a^2)dx=log #10;| ...

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Functions

∫ 1 √ 2-x 2 ...

Question

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

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Solution

We have,

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

Now,

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

Using $\int \frac{1}{\sqrt{x^{2} + a^{2}}} d x = log ∣ ∣ x + \sqrt{x^{2} + a^{2}} ∣ ∣$

So,

$\int \frac{1}{\sqrt{(2 - x^{2}) + 1^{2}}} d x = log ∣ ∣ ∣ (2 - x) + \sqrt{{(2 - x)}^{2} + 1} ∣ ∣ ∣$
Hence, this is the answer.

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