Mathematics

$$\int { \cfrac { \left( x+3 \right) { e }^{ x } }{ { \left( x+4 \right)  }^{ 2 } } dx } =$$


SOLUTION
$$I=\int \frac{(x+3)e^{x}}{(x+4)^{2}}dx$$
$$I=\int \frac{(x+4-1)e^{x}}{(x+4)^{2}}dx$$
$$I=\int \frac{e^{x}}{(x+4)}dx-\int \frac{e^{x}}{(x+4)^{2}}dx$$
$$I=\int \frac{e^{x}}{(x+4)}dx-e^{x}[\frac{-1}{(x+4)}]-\int e^{x}(\frac{-1}{(x+4)})dx$$
$$I=\int \frac{e^{x}dx}{(x+4)}+[\frac{e^{x}}{(x+4)}]-\int \frac{e^{x}}{(x+4)}dx$$
$$I=\frac{e^{x}}{x+4}+c$$
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Subjective Medium Published on 17th 09, 2020
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