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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS2 Marks
Question
Evaluate the following integrals:
$\int\Big(\frac{\text{m}}{\text{x}}+\frac{\text{x}}{\text{m}}+\text{m}^\text{x}+\text{x}^\text{m}+\text{mx}\Big)\text{dx}$
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Answer

$\int\Big(\frac{\text{m}}{\text{x}}+\frac{\text{x}}{\text{m}}+\text{m}^\text{x}+\text{x}^\text{m}+\text{mx}\Big)\text{dx}$
$=\text{m}\int\frac{1}{\text{x}}\text{dx}+\frac{1}{\text{m}}\int\text{xdx}+\int\text{m}^\text{x}\text{dx}\int\text{x}^\text{m}\text{dx}+\text{m}\int\text{xdx}$
$=\text{m}\log|\text{x}|+\frac{\text{x}^2}{2\text{m}}+\frac{\text{m}^\text{x}}{\log\text{m}}+\frac{\text{x}^{\text{m}+1}}{\text{m}+1}+\frac{\text{mx}^2}{2}+\text{C}$

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