Question

How do you integrate le="(3x^{2} + 3) ^{3} " alt="(3x^{2} + 3) ^{3} " align="absmiddle" class="latex-formula">
?​

Answer 1

Answer:

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

Step-by-step explanation:

$(3x^2 + 3)^3 = (3x^2)^3 + 3^3 + 3((3x^2)^2)(3) + 3(3x^2)(3^2)$

              $= 27x^6 + 27 + 3(9x^4 \times 3) + 3(3x^2 \times 9)\\\\=27x^6 + 27 + 81x^4 + 81x^2\\\\=27x^6 + 81x^4 + 81x^2 + 27$

$\int\limits {(3x^2+3)^3} \, dx = \int\limits {27x^6 + 81x^4+81x^2 + 27} \, dx$

                      $= \frac{27}{7}x^7 + \frac{81}{5}x^5+\frac{81}{3}x^3 + 27x +C\\\\= \frac{27}{7}x^7 + \frac{81}{5}x^5+27x^3 + 27x +C$