Question

How do you integrate (3^xdx)/(3^x - 7) ?

Answer 1

\[\int \frac{3^x}{3^x - 7}dx \]

Answer 2

the top is the derivative of the bottom except for a constant

Answer 3

\[Dx(3^x)=3^x\ ln(3)\]

Answer 4

multiply this by \(\cfrac{ln(3)}{ln(3)}\) and use what you need and pull out the rest as a constatnt

Answer 5

\[\frac{1}{ln(3)}\ \int \frac{3^x\ ln(3)}{3^x - 7}dx=\frac{ln|3^x -7|}{ln(3)}\]

Answer 6

+C ...

Answer 7

lol...don't forget the plus see

Answer 8

one way to do this is to go ... i have to use a "u" and if i dont then it cant be done ::: arms flailing and spittle flying:::

Answer 9

lol spittle

Answer 10

u = 3^x - 7

du = 3^x ln(3) dx

dx = du/3^x ln(3)

\[\int \frac{3^x}{3^x\ ln(3)\ u}du\]
\[\int \frac{\cancel{3^x}}{\cancel{3^x}\ ln(3)\ u}du\]
\[\int \frac{1}{\ ln(3)\ u}du\]
\[\frac{1}{ln(3)}\int \frac{1}{u}du\]

Answer 11

i perfer the first method, since it doesnt waste as much time :)