antiderivative/integration

[brittini14]

integrate (2x^2+6)^4(x)

 

[Deleted member 4993]

integrate (2x^2+6)^4(x)

Is it

x * (2x^2+6)^4 dx

or

(2x^2+6)^(4x) dx

 

[skeeter]

let \(\displaystyle \L u = 2x^2 + 6\)
\(\displaystyle \L du = 4x dx\)

\(\displaystyle \L \int x(2x^2 + 6)^4 dx\)

\(\displaystyle \L \frac{1}{4} \int 4x(2x^2 + 6)^4 dx\)

substitute ...

\(\displaystyle \L \frac{1}{4} \int u^4 du\)

can you finish integrating and performing the back-substitution?