Evaluate the following integrals: (2^ x +5 x -1 x^ 1 3 )dx - Vidyadip

Question

Evaluate the following integrals:
$\int\bigg (2^{\text{x}}+\frac{5}{\text{x}}-\frac{1}{\text{x}^{\frac{1}{3}}}\bigg)\text{dx}$

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Answer

$\int\bigg(2^{\text{x}}+\frac{5}{\text{x}}-\frac{1}{\text{x}^{\frac{1}{3}}}\bigg)\text{dx}$
$=\int2^{\text{x}}\text{dx}+5\int\frac{1}{\text{x}}\text{dx}-\int\frac{1}{\text{x}^{\frac{1}{3}}}\text{dx}$
$=\frac{2^{\text{x}}}{\log2}+5\log\text{x}-\frac{3}{2}\text{x}^{\frac{2}{3}}+\text{C}$

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