Question

How do you integrate7^2x

Answer 1

\[\int b^xdx=\frac{b^x}{\ln(b)}\] is good to know in general

Answer 2

i guess you also need the chain rule aka u substitution because you have \(\int 7^{2x}dx\) but that is a small challenge , make \(u=2x.\frac{1}{2}du = dx\) etc

Answer 3

Could you go through the u substitution please. I have trouble with that

Answer 4

\[u=2x, du = 2xdx,\frac{1}{2}du=dx\] you get
\[\int7^{2x}dx=\frac{1}{2}\int 7^udu=\frac{7^u}{2\ln(7)}=\frac{7^{2x}}{2\ln(7)}\]

Answer 5

sorry first line should be \(u=2x,du=2dx\)

Answer 6

ok thanks a lot.

Answer 7

yw