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∫ 2 X 4 + 7 X 3 + 6 X 2 X 2 + 2 X D X - Mathematics

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प्रश्न

\[\int\frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} dx\]
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उत्तर

\[\int\left( \frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} \right)dx\]
\[ = \int \frac{x^2 \left( 2 x^2 + 7x + 6 \right)}{x\left( x + 2 \right)}dx\]
\[ = \int\frac{x\left[ 2 x^2 + 4x + 3x + 6 \right]}{x + 2}dx\]
\[ = \int\frac{x\left( 2x\left( x + 2 \right) + 3\left( x + 2 \right) \right)}{\left( x + 2 \right)}dx\]

`= c x ( (2x+3)(x+2)) / (x+2) dx` 


\[ = \int\left( 2 x^2 + 3x \right)dx\]
` = 2   ∫  x^2 dx + 3∫   x    dx`
\[ = 2\left[ \frac{x^3}{3} \right] + 3\left[ \frac{x^2}{2} \right] + C\]
\[ = \frac{2}{3} x^3 + \frac{3}{2} x^2 + C\]

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अध्याय 19: Indefinite Integrals - Exercise 19.02 [पृष्ठ १५]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Exercise 19.02 | Q 19 | पृष्ठ १५

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