Evaluate the following integrals: x^2+e^ + ( e 2 )^x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\bigg\{\text{x}^2+\text{e}^{\log\text{x}}+\Big(\frac{\text{e}}{2}\Big)^\text{x}\bigg\}\text{dx}$

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Answer

$\int\bigg\{\text{x}^2+\text{e}^{\log\text{x}}+\Big(\frac{\text{e}}{2}\Big)^\text{x}\bigg\}\text{dx}$
$=\int\text{x}^2\text{dx}+\int\text{e}^{\log\text{x}}\text{dx}+\int\Big(\frac{\text{e}}{2}\Big)^\text{x}\text{dx}$
$=\frac{\text{x}^3}{3}+\int\text{xdx}+\int\Big(\frac{\text{e}}{2}\Big)\text{dx}$
$=\frac{\text{x}^3}{3}+\frac{\text{x}^2}{2}+\frac{1}{\log\big(\frac{\text{e}}{2}\big)}\times\Big(\frac{\text{e}}{2}\Big)^\text{x}+\text{C}$

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