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MIT 8.01 Physics I Classical Mechanics, Fall 1999
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OpenStudy (anonymous):
I am trying to integrate (3x)(1+(x^2))^(1/2). Using integration by parts, I get u as 3x, du as 3 dx and dv comes as (1+(x^2)). To find v, I integrate dv and v comes out to be (1+(x^2))^(3/2) divided by 3x. I use the formula for integration by parts and get the answer. But it is not the correct answer. Why? http://www.wolframalpha.com/input/?i=Integrate+%283x%29%28%281%2Bx%5E%282%29%29%5E%281%2F2%29
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OpenStudy (anonymous):
Its just a simple substitution. Let w=1+x^2, dw=2xdx, 3/2 dw = 3x dx Now you have \[ \int\limits_{}^{} (3/2) w ^{1/2} dw\] just a simple power rule. then remember to replace w with 1+x^2.
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