Tuesday, 6 October 2015

calculus - Integral without using substitution method.

How to solve this integral without using substitution method? As I'm curious that is there another method to solve integral? I did integration by parts.




4x2dx=x4x2+x24x2dx
=x4x24x24x2dx+44x2dx
=x4x24x2dx+4sin1(x2)
24x2dx=x4x2+4sin1(x2)
4x2dx=12x4x2+2sin1(x2)



Is there any other method can solve integral other than substitution and this? I think Riemann Sum also can be used to solved. But people riemann sum is not considered a method of integration. I wonder why. Thanks a lot.

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