Mathematics

solve
$$\displaystyle \int e^{x} \dfrac{2+x}{(3+x)^{2}} dx$$.


SOLUTION
We have,
$$\int {{e^x}\frac{{2 + x}}{{{{\left( {3 + x} \right)}^2}}}dx} $$
$$\begin{array}{l} =\int { { e^{ x } }\left[ { \frac { { \left( { 3+x } \right) -1 } }{ { { { \left( { 3+x } \right)  }^{ 2 } } } }  } \right] dx }  \\ =\int { { e^{ x } }\left[ { \frac { 1 }{ { 3+x } } -\frac { 1 }{ { { { \left( { 3+x } \right)  }^{ 2 } } } }  } \right] dx }  \\ =\frac { { { e^{ x } } } }{ { 3+x } } +C \end{array}$$
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Subjective Medium Published on 17th 09, 2020
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