Integrate sqrt(x)csc^2[x^(3/2)]dx

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- May 17th 2006, 11:53 AMbobby77please need help-urgent
Integrate sqrt(x)csc^2[x^(3/2)]dx

- May 17th 2006, 12:38 PMtopsquarkQuote:

Originally Posted by**bobby77**

Let $\displaystyle y = x^{3/2}$

Thus $\displaystyle dy = \frac{3}{2} \sqrt{x}\, dx$

$\displaystyle \int dx \, \sqrt{x} \, csc^2 \left ( x^{3/2} \right ) = \frac{2}{3} \int dy \, csc^2(y)$

$\displaystyle = -\frac{2}{3}cot(y) = -\frac{2}{3} cot \left ( x^{3/2} \right )$

-Dan - May 17th 2006, 12:48 PMCaptainBlackQuote:

Originally Posted by**bobby77**

$\displaystyle \frac{d}{dx} \left(\frac{2}{3} x^{3/2}\right) =x^{1/2}$, so the

integrand is the derivative of a multiple of $\displaystyle \cot(x^{3/2}) $.

From here the fundamental theorem of Calculus should give you the answer.

RonL - May 17th 2006, 12:54 PMtopsquarkQuote:

Originally Posted by**topsquark**

-Dan