jasongggg
Answered

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How do you integrate
[tex](3x^{2} + 3) ^{3} [/tex]
?​

How Do You Integrate Tex3x2 3 3 Tex class=

Sagot :

sreedevi102

Answer:

Since i don't know what formula is mentioned. I just used the easiest way to solve :)

Step-by-step explanation:

[tex](3x^2 + 3)^3 = (3x^2)^3 + 3^3 + 3((3x^2)^2)(3) + 3(3x^2)(3^2)[/tex]

              [tex]= 27x^6 + 27 + 3(9x^4 \times 3) + 3(3x^2 \times 9)\\\\=27x^6 + 27 + 81x^4 + 81x^2\\\\=27x^6 + 81x^4 + 81x^2 + 27\\\\[/tex]

[tex]\int\limits {(3x^2+3)^3} \, dx = \int\limits {27x^6 + 81x^4+81x^2 + 27} \, dx[/tex]

                      [tex]= \frac{27}{7}x^7 + \frac{81}{5}x^5+\frac{81}{3}x^3 + 27x +C\\\\= \frac{27}{7}x^7 + \frac{81}{5}x^5+27x^3 + 27x +C\\\\[/tex]

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