मराठी

∫x3x+1 is equal to ______. - Mathematics

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प्रश्न

`int x^3/(x + 1)` is equal to ______.

पर्याय

  • `x + x^2/2 + x^3/3 - log|1 - x| + "C"`

  • `x + x^2/2 - x^3/3 - log|1 - x| + "C"`

  • `x - x^2/2 - x^3/3 - log|1 + x| + "C"`

  • `x - x^2/2 + x^3/3 - log|1 + x| + "C"`

MCQ
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उत्तर

`int x^3/(x + 1)` is equal to `x - x^2/2 + x^3/3 - log|1 + x| + "C"`.

Explanation:

I = `int x^3/(x + 1)`

= `int (x^3 + 1 - 1)/(x + 1) "d"x`

= `int (x^3 + 1)/(x + 1) "d"x - int 1/(x + 1) "d"x`

= `int (x^2 - x + 1)"d"x - int 1/(x + 1) "d"x`

= `x^3/3 - x^2/2 + x - log|x + 1| + "C"`

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Definite Integrals
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पाठ 7: Integrals - Exercise [पृष्ठ १६८]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 7 Integrals
Exercise | Q 54 | पृष्ठ १६८

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