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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

∫x7(1+x4)2 dx - Mathematics and Statistics

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प्रश्न

`int x^7/(1 + x^4)^2  "d"x`

बेरीज
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उत्तर

Let I = `int x^7/(1 + x^4)^2  "d"x`

= `int (x^4*x^3)/(1 + x^4)^2  "d"x`

Put 1 + x4 = t

∴ 4x3 dx = dt

∴ x3 dx = `1/4  "dt"`

∴ I = `1/4 int (("t" - 1))/"t"^2  "dt"`

= `1/4(int 1/"t" "dt" -int 1/"t"^2  "dt")`

= `1/4[log|"t"| - "t"^-1/(-1)] + "c"`

∴ `1/4[log|1 + x^4| + 1/(1 + x^4)] + "c"`

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पाठ 2.3: Indefinite Integration - Short Answers I

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