Question

Please help me solve the following integral (click to see).

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ \sqrt{x}3^{\sqrt{x}} }dx\]

Answer 2

\[\text{Let $u=\sqrt{x}$}\]

Answer 3

\[dx=\frac{ du }{ \frac{ 1 }{ 2 \sqrt{x} } }\]

Answer 4

\[2\int\limits_{}^{}\frac{ 1 }{ 3^{u} }du\]

Answer 5

I'm stuck here

Answer 6

You can write it as\[\int3^{-u}du\]
Then,
\[\begin{align*}3^{-u}&=\large e^{\ln{3^{-u}}}\\
&=\large e^{-u \ln3}\end{align*}\]
Now your integral becomes
\[\int\large e^{-u \ln3}du\]
Make another substitution:
\[t=-u\ln3\]

Answer 7

ok thanks

Answer 8

the two remains out-front, correct?

Answer 9

Yeah, sorry I left it out.