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Integrate the functions.$$(4 x+2) \sqrt{x^{2}+x+1}$$
01:57
Suman Saurav T.
Calculus 2 / BC
Chapter 7
Integrals
Section 2
Integration as an Inverse Process of Differentiation
Integration Techniques
Baylor University
University of Nottingham
Boston College
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in this question we have to find the undeveloped function for express to Okay, multiplied red under root X square plus X plus one. Let us write the X. Here. And then details in here. Note that this integration can be written us to multiplied with two X plus one. Underwrote X square plus expressed one. So now let us make this substitution Under route X square plus X plus one is equal to T. Then squaring both sides, gives X squared plus X plus one is equal to b squared. Differentiating both the sides. We get two X plus one. The X is equal to duty duty. So substituting the value back and then detail. We get integration of. Can we take an outside and the root X squared plus X plus one is T multiplied with two. X plus one. Paired with the eggs will be to T. D. P. So this will give four Underwrote p square Bp which is equal to four divided by three D cube plus a constant of integration, Capital C. Substituting back the value of T. We get. The final answer has four divided by three under route X square plus X plus Fun. All race to the par three plus capital C.
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