Problem

Integrate the functions. $$ x \sqrt{1+2 x^{2}} $$

01:21

Problem 7 Easy Difficulty

Integrate the functions.
$$
x \sqrt{x+2}
$$

Answer

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Video Transcript

in this question we are required to integrate the function X. Under route X plus two. So let us write the exhale and then people sign here we will make the substitution. And the route takes plus two is equal to feet. So taking square on both sides. We get X plus two is equal to T square differentiating both sides. We get the X. Is equal to to be Bt. So let us make the substitution. This will be equal to integrate off. Now X can be written us T square minus two, multiplied with and the root expressed to his P. And then the exist to D. D. P. So this can be lit in us integral off to take an outside be square P square minus two baby. Let us open the bracket to get the raise to depart four minus two. Multiplied with the race to the part two baby. Now we can break this integral into two parts as to integral of serious to the par 4 80 minus four integral locked areas to the to Bt. Let us simplify these integral size to multiply with three days to the par five divided by five minus four. Multiplied bed theory to the battery, divided by three plus a constant of integration Capital C. No, since P is equal to and Rudolph express to. So let's substitute these values back to get the final answer as to divided by five. Underwrote X plus two, always to the par five minus four, divided by three and the root X plus two. Place to the par three plus capital C.

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