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Question

1x(xn+1)dx.

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Solution

(1x(xn+1))dx=(xn1xn(xn+1))dxletxn=tnxn1dx=dtxn1dx=(dtn)I=(1n)(1t(t+1)dt)=(1n)[(1t)dt(1t+1)dt]=(1n)[logtlog(t+1)]+c=(1n)log((1n))+c=(1n)log((xnxn+1))+c


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