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INTEGRALS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINTEGRALS2 Marks
Question
Integrate the function in Exercise:
$\frac{\text{e}^{5\log\text{x}}-\text{e}^{4\log\text{x}}}{\text{e}^{3\log\text{x}}-\text{e}^{2\log\text{x}}}$
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Answer

$\frac{\text{e}^{5\log\text{x}}-\text{e}^{4\log\text{x}}}{\text{e}^{3\log\text{x}}-\text{e}^{2\log\text{x}}}=\frac{\text{e}^{4\log\text{x}}\big(\text{e}^{\log\text{x}}-1\big)}{\text{e}^{2\log\text{x}}\big(\text{e}^{\log\text{x}}-1\big)}$$=\text{e}^{2\log\text{x}}$
$=\text{e}^{\log\text{x}^{2}}$
$=\text{x}^{2}$
$\therefore\int\frac{\text{e}^{5\log\text{x}}-\text{e}^{4\log\text{x}}}{\text{e}^{3\log\text{x}}-\text{e}^{2\log\text{x}}}\text{dx}=\int\text{x}^{2}\text{dx}=\frac{\text{x}^{3}}{3}+\text{C}$

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