题目
多项填空题
Question textEvaluate the indefinite integral\displaystyle \dfrac{2}{x(x+2)}\,dx.The result can be written in the formA\ln|x| + B\ln|x+2| +C where A and B are integers, and C is a constant of integration. Fill in the correct responses for A and B. A= Answer 1 Question 19[input] B = Answer 2 Question 19[input].
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思路分析
The problem asks us to evaluate the integral 2/(x(x+2)) dx and express the result in the form A ln|x| + B ln|x+2| + C, where A and B are integers.
First, decompose the ratio......Login to view full explanation登录即可查看完整答案
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Question textThe function f(x)=\dfrac{x+2}{(x+1)(x-1)^2} can be resolved into partial fractions of the form:\dfrac{a}{x+1} + \dfrac{b}{x-1} + \dfrac{c}{(x-1)^2}where a,\,b and c are real number values.Use this to express \displaystyle \int f(x)\,dx in the form\displaystyle \int f(x)\,dx = \dfrac{1}{A}\ln|x+1|+\dfrac{1}{B}\ln|x-1| + \dfrac{D}{2x-2}+ C.where A,\,B and D are integer values, and C is a constant of integration.Fill in the correct values for A,\,B, and D.A = Answer 1 Question 23[input] B = Answer 2 Question 23[input] D = Answer 3 Question 23[input]
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