Consider the following definite integral 1 xx+1dx 1. Why can't we apply any of our known...

 

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Consider the following definite integral 1 xx+1dx 1. Why can't we apply any of our known integral functions to find the antiderivative? 2. If we pick u= x + 1, then du = dx. At first glance, this doesn't seem to work. From our usual examples, why would it seem that substitution wont work? 3. Substitution does work but in a slightly different way. Let u = x + 1. And thus, x = u - 1 and du = dx. Make these three substitution into the definite integral and find the value of the integral. Consider the following definite integral 1 xx+1dx 1. Why can't we apply any of our known integral functions to find the antiderivative? 2. If we pick u= x + 1, then du = dx. At first glance, this doesn't seem to work. From our usual examples, why would it seem that substitution wont work? 3. Substitution does work but in a slightly different way. Let u = x + 1. And thus, x = u - 1 and du = dx. Make these three substitution into the definite integral and find the value of the integral.