IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

chemicaltester

x^5/2 /(x^7/2 + x^6)
put x^7/2 =t
hence 7/2 *x^5/2 dx =dt
also x^6 =x^12/2 = ( x^7/2)^5/2

hence equation becomes

dt /t +t^5/2
=dt/t(1 +t^3/2)
i think we have to further substitue
adjesting numerator as t^1/2 +1 -t^1/2 we can do that

if this gives answer do rate me
if this then somebody please help both of us

konichiwa2x

edit: removed solution on radon's request. Open for others to try.

raulrag009

Here is my solution

$\int{\frac{x^{\frac{5}{2}}}{x^{\frac{7}{2}}+x^{6}}}dx\\\\ \int{x^{\frac{-7}{2}}(1+x^{\frac{-5}{2}})^{\frac{-1}{2}}}dx\\\\ Put\;1+x^{\frac{-5}{2}}=t^{2}\\\\ x^{\frac{-7}{2}}dx=\frac{4}{5}tdt\\\\ \frac{4}{5}\int{dt}\\\\ =\frac{4t}{5}+C\\\\ =\frac{4}{5}(1+x^{\frac{-5}{2}})^{\frac{1}{2}}+C$

Radon222

rahul your answer is perfect except a small negative sign mistake in the end

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