integration of x square divided by under root (1+x)
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integration of x square divided by under root (1+x)
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Let x=sinθ⟹dx=cosθ dθ
∴∫1−x2√x dx=∫1−sin2θ√sinθcosθ dθ
=∫cosθsinθcosθ dθ
=∫cos2θsinθ dθ
=∫1−sin2θsinθ dθ
=∫cscθ dθ−∫sinθ dθ
=ln|cscθ−cotθ|+cosθ+C
=ln∣∣∣1x−1−x2√x∣∣∣+1−x2−−−−−√+C
=ln∣∣∣1−1−x2√x∣∣∣+1−x2−−−−−√+C