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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Integrate the following with respect to the respective variable: x7x+1

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प्रश्न

Integrate the following with respect to the respective variable:

`x^7/(x + 1)`

बेरीज
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उत्तर

Let I = `int x^7/(x + 1)*dx`

= `int ((x^7 + 1) - 1)/(x + 1)*dx`

= `int ((x + 1)(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1) - 1)/(x + 1)*dx`

= `int [x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 - (1)/(x + 1)]*dx`

= `int x^6 dx - intx^5 dx + intx^4 dx - intx^3 dx + intx^2 dx - intx dx + int1 dx - int (1)/(x + 1) dx`

= `x^7/(7) - x^6/(6) + x^5/(5) - x^4/(4) + x^3/(3) - x^2/(2) + x - log|x + 1| + c`.

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पाठ 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १५०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 2.2 | पृष्ठ १५०

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