Question

Integrate sin sqrt(x) / [x cos^3 sqrt(x)]
any idea how?

Answer 1

Firstly, I need to see the parenthesis for your sin, because it is ambiguous as it is. Secondly, are you given specific endpoints? Is it from negative infinity to infinity? Or is this just an indefinite integral?

Thank you!

Answer 2

indefinite integral, \[\int\limits_{}^{} \sin \sqrt{x} / \sqrt{x \cos ^{3}\sqrt{x}}\]
sorry this is the question :)

Answer 3

Ouch. Well you can take the derivative of the bottom. If that's equal to the top, then the integral is just ln(bottom). [where ln is the natural logarithm].

Unfortunately it doesn't look like the derivative of the bottom is the top. You see that cos^2 is in the bottom, so you can pull that part out of the square root. Then you might look at it as tan(sqrt(x)) / (sqrt(x)*cos(sqrt(x))), and again try the same trick.

I'm afraid these attempts may not work out, but you have to try these things anyway. Soon enough you'll find something that works...

Answer 4

\[\int\limits{\frac{\sin(\sqrt{x})}{\sqrt{x}\cos^{\frac{3}{2}}(\sqrt{x})}}dx\]
let u=cos sqrt(x)
du=-sin(sqrt(x)/(2sqrt(x))

so the integral becomse\[-2 \int\limits{\frac{1}{u^{\frac{3}{2}}}}du\]\[=\frac{4}{\sqrt{u}}+C\]now substitute u=cos(Sqrt(x)) back

Answer 5

\[=\frac{4}{\sqrt{\cos(\sqrt{x})}}+C\]

Answer 6

yeap. @Sarah.L thats the answer. may i know how u did it?

Answer 7

i showed u the steps !!
use substitution

Answer 8

oh sorry. did not see it, thanks so much! :)

Answer 9

:)