+9466 Is this your integral?
\(\displaystyle\int9(3x+10)^6 dx\)
If so....
Let's pick u = 3x + 10 which means du = 3 dx and then substitute these in like this:
\(\phantom{=\quad}\displaystyle\int9(3x+10)^6 dx\\~\\ {=\quad}\displaystyle\int3\cdot3(3x+10)^6 dx\\~\\ {=\quad}3\displaystyle\int(3x+10)^6 \cdot 3dx\\~\\ {=\quad}3\displaystyle\int u^6 \cdot du \\~\\ {=\quad}3\displaystyle\int u^6 du\)
Now we can use the rule which says \(\int u^n du\ =\ \frac{u^{n+1}}{n+1}+c\) to get...
\({=\quad}3\cdot\frac{u^7}{7}+c\\~\\ {=\quad}\frac37u^7+c\)
Now let's substitute 3x + 10 back in for u
\({=\quad}\frac37(3x+10)^7+c\)
