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

Question

babyslapmafro · Answer

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

anonymous · Answer

Let u = √x

babyslapmafro · Answer

which one

anonymous · Answer

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

babyslapmafro · Answer

how do you solve 3^u

anonymous · Answer

$$\large 3^{u}=e^{\ln(3^u)}=e^{u\ln3}$$
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.

anonymous · Answer

**Should be a minus in the exponent.

babyslapmafro · Answer

oh ok thanks

babyslapmafro · Answer

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

anonymous · Answer

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