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integration
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Use of substitution u=1/x to find ∫[√(1-x^2)/x^4]dx
最佳解答:
The integral is straightforward as follow: 圖片參考：http://i187.photobucket.com/albums/x22/cshung/7007101504798.jpg 2007-10-16 21:59:29 補充： Ooops... a little bit slower, remember to add the constant C.
其他解答:
Use of substitution u=1/x to find ∫[√(1-x^2)/x^4]dx u=1/x;x=1/u x^2=1/u^2;x^4=1/u^4 dx=(-1/u^2)du ∫[√(1-x^2)/x^4]dx =∫[u^4√(1-1/u^2)](-1/u^2)du =-∫{u^2√[(u^2-1)/u^2]}du =-∫u√(u^2-1)du =-(1/2)∫√(u^2-1)d(u^2-1) =-(1/3)(u^2-1)^(3/2)+C =-(1/3)(1/x^2-1)^(3/2)+C
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