How do you integrate (3x^(2) + 3) ^(3) ?​

Question

How do you integrate

`(3x^(2) + 3) ^(3)`
?​

Answer 1

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

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 * 3) + 3(3x^2 * 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`

`= (27)/(7)x^7 + (81)/(5)x^5+(81)/(3)x^3 + 27x +C\\\\= (27)/(7)x^7 + (81)/(5)x^5+27x^3 + 27x +C\\\\`