Question

Compute the following integral ∫ 6^(x) /4^(x-1) dx ?

Answer 1

\[\int\limits \frac{ 6^x }{ 4^{x-1} }dx=\int\limits \frac{ 6^x }{ 4^x*4^{-1}}dx=4 \int\limits \left( \frac{ 6 }{ 4 } \right)^x dx=?\]
\[\int\limits a^x dx=\frac{ a^x }{ \log a }\]

Answer 2

4 integral (3/2)^x / ln(3/4) + C @surjithayer I'm cofused as to what happens to the 4 outside the integral, could you please explain ?

Answer 3

you are mistaken.
\[4 \int\limits \left( \frac{ 3 }{ 2 } \right)^xdx=4 \frac{ \left( \frac{ 3 }{ 2 } \right)^x }{ \ln \left( \frac{ 3 }{ 2 } \right)}+c\]

Answer 4

Oh okay thank you for explaining !

Answer 5

yw