Question

Please help me get started on the following integral (click to see).

Answer 1

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

Answer 2

Let u = √x

Answer 3

which one

Answer 4

Well, both √x's are the same, but the one in the exponent will remain after the substitution:\[u=\sqrt x\\
du=\frac{1}{2\sqrt x}dx\\
2\;du=\frac{1}{\sqrt x}dx\]
\[\int\frac{1}{3^u}du\]

Answer 5

how do you solve 3^u

Answer 6

\[\large 3^{u}=e^{\ln(3^u)}=e^{u\ln3}\]
So, your integral changes to
\[\int e^{u\ln3}du\]
You'll have to make another substitution, unless you know the formula for integrals of exponentials with base not = e.

Answer 7

**Should be a minus in the exponent.

Answer 8

oh ok thanks

Answer 9

also, i believe there is a 2 in front of the integral after you make the first substitution

Answer 10

Yes, that too. Sorry I didn't keep track of it.