To solve: $ I=\int \frac{(1+x)e^x}{(2+x)^2} \,dx. $ We have a ready formula as \int e^x[f(x)+f'(x)]\,dx= e^x f(x). My question is how to find $f(x)$ from the given function in question such that we have f'(x) available with us?
solve $\int(1+x)e^x/(2+x)^2\,dx$
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calculus
1 Answers
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\frac{1+x}{(x+2)^2} = \frac{x+2 -1}{(x+2)^2} = \frac{1}{x+2} - \frac{1}{(x+2)^2} = \frac{1}{x+2} + \left( \frac{1}{x+2} \right)'