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प्रश्न
Evaluate: `int "x" * "e"^"2x"` dx
उत्तर
Let I = `int "x" * "e"^"2x"` dx
`= "x" int "e"^"2x" "dx" - int["d"/"dx" ("x") int "e"^"2x" * "dx"]` dx
`= "x" * "e"^"2x"/2 - int 1 * "e"^"2x"/2` dx
`= 1/2 "xe"^"2x" - 1/2 int "e"^"2x"` dx
`= 1/2 "x e"^"2x" - 1/2 * "e"^"2x"/2` + c
∴ I = `1/4 "e"^"2x" ("2x" - 1)` + c
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