Question

HELP PLEASE
integrate ((1+3sqrt(x))^4)/sqrt(x)

Answer 1

Hint :
There is a very obvious substitution

Answer 2

I'm not the ebst at u substitutions but my teacher said that it would be easy if u=sqrt(x) and du=1/(2sqrt(x))

Answer 3

that works, but there is even a better substitution

Answer 4

\[\int\limits \frac{(1+3\sqrt{x})^4}{\sqrt{x}}dx\]
Re writing some things makes it more easier to notice the substitution
\[2 \int\limits (1+3\sqrt{x})^4 .\frac{dx}{2\sqrt{x}}\]

Answer 5

Can I substitute u=1+3sqrt(x)?

Answer 6

yes!

Answer 7

Infact one more step you could do
\[\frac{2}{3} \int\limits (1+3\sqrt{x})^4.\frac{3dx}{2\sqrt{x}}\]

Answer 8

Try the substitution you were talking about

Answer 9

I'm confused as to what I'm supposed to do with the \[(3dx)/(2\sqrt{x})\] part.

Answer 10

I get that if I integrate u^4 I get (1/5)u^5 though

Answer 11

\[u=1+3\sqrt{x}\]
Find the derivative with respect to x, you'll see why I did that shortly

Answer 12

Ok I get \[\frac{ 3 }{ 2\sqrt{x} }\]

Answer 13

\[\frac{du}{dx}=\frac{3}{2\sqrt{x}}\]\[du=\frac{3}{2\sqrt{x}}dx\]