(e^ x +1)^2e^ x dx - Vidyadip

Question

$\int(\text{e}^{\text{x}}+1)^2\text{e}^{\text{x}}\text{ dx}$

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Answer

Consider $\text{I}=\int(\text{e}^{\text{x}}+1)^2\text{e}^{\text{x}}\text{dx}$
Let $(\text{e}^{\text{x}}+1)=\text{t}\rightarrow\text{e}^{\text{x}}\text{dx}=\text{dt}$
$\text{I}=\int(\text{e}^\text{x}+1)^2\text{e}^{\text{x}}\text{dx}$
$=\int(\text{t})^2\text{dt}$
$=\frac{\text{t}^3}{3}+\text{c}$
$=\frac{(\text{e}^{\text{x}}+1)^3}{3}+\text{c}$

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