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Evaluate: ∫ex1+x/(2+x)2 dx - Mathematics and Statistics

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प्रश्न

Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx

योग
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उत्तर

Let I = `int "e"^"x" (1 + "x")/(2 + "x")^2` dx

`= int "e"^"x" [((2 + "x") - 1)/(2 + "x")^2]` dx

`= int "e"^"x" [1/(2 + "x") - 1/(2 + "x")^2]`dx

Let f(x) = `1/(2 + "x")`

∴ f '(x) = `(-1)/(2 +"x")^2`

∴ I = `int "e"^"x" ["f"("x") + "f" '("x")]` dx

`= "e"^"x" * "f"("x") + "c"`

`= "e"^"x" * 1/(2 + "x")` + c

∴ I = `"e"^"x"/(2 + "x")` + c

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Integration - MISCELLANEOUS EXERCISE - 5 [पृष्ठ १३९]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 5 Integration
MISCELLANEOUS EXERCISE - 5 | Q IV. 4) ii) | पृष्ठ १३९

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