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Ali E.

asked • 10/09/17

Use substitution x=sin theta to evaluate integrate x^2/(1-x^2)^5/2

Full working out please

2 Answers By Expert Tutors

By:

Andy C. answered • 10/09/17

Tutor
4.9 (27)

Math/Physics Tutor

Michael J. answered • 10/09/17

Tutor
5 (5)

Mastery of Limits, Derivatives, and Integration Techniques

Andy C.

 
OK Ali, two tutors , Michael J and myself agree on the answer.
 
His answer is the same.
Recall that arcsin X = theta, the angle. 
Or as I call it, arcsin X = T
 
His answer becomes 1/3 (tan T) ^3.
 
Using the same trigonometric argument I have in my solution,
the tangent of the angle is x/sqrt(1-x^2).
 
This results in the same answer, as shown.
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10/09/17

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