OpenStudy (anthonyn2121):

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

1 year ago
ganeshie8 (ganeshie8):

Hint : There is a very obvious substitution

1 year ago
OpenStudy (anthonyn2121):

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))

1 year ago
ganeshie8 (ganeshie8):

that works, but there is even a better substitution

1 year ago
OpenStudy (anonymous):

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

1 year ago
OpenStudy (anthonyn2121):

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

1 year ago
OpenStudy (anonymous):

yes!

1 year ago
OpenStudy (anonymous):

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

1 year ago
OpenStudy (anonymous):

Try the substitution you were talking about

1 year ago
OpenStudy (anthonyn2121):

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

1 year ago
OpenStudy (anthonyn2121):

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

1 year ago
OpenStudy (anonymous):

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

1 year ago
OpenStudy (anthonyn2121):

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

1 year ago
OpenStudy (anonymous):

\[\frac{du}{dx}=\frac{3}{2\sqrt{x}}\]\[du=\frac{3}{2\sqrt{x}}dx\]|dw:1448776991550:dw|

1 year ago