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Choose the correct alternative from the following. xxxx + 1dx∫(x3+3x2+3x+1)(x + 1)5 dx = - Mathematics and Statistics

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प्रश्न

Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 

विकल्प

  • `(-1)/"x + 1"` + c

  • `((-1)/"x + 1")^5` + c

  • log(x + 1) + c

  • log |x + 1|5 + c 

MCQ
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उत्तर

`(-1)/"x + 1"` + c

Explanation:

= `int ("x + 1")^3/("x + 1")^5` dx

∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3

(x + 1)3 = x3 + 3x2 + 3x + 1

= `1/((x + 1)^2) dx`

= `int (x + 1)^-2 . dx`

= `(x + 1)^(-2 + 1)/-2 + 1 + c`

= `(x + 1)^-1/-1 + c`

= `(-1)/(x + 1) + c`

`= (-1)/"x + 1"` + c

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अध्याय 5: Integration - MISCELLANEOUS EXERCISE - 5 [पृष्ठ १३८]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 5 Integration
MISCELLANEOUS EXERCISE - 5 | Q I. 10) | पृष्ठ १३८

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