Integrate the function in x2ex. - Mathematics

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Sum

Integrate the function in `x^2e^x`.

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Solution

Let `I = int x^2 e^x dx`

Put u = x2, v = ex 

`int uv  dx = u int v  dx - int( (du)/dx int v  dx) dx`

`= x^2 int e^x dx - int (2x).e^x dx`

`= x^2 e^x - 2 int xe^x dx`

We define the first function by integrating multiple parts.

`I = x^2 e^x - 2 [x int e^x  dx - int (d/dx  x. int e^x  dx)]`

`= x^2 e^x - 2 [xe^x - 2 int 1.e^x dx]`

`= x^2 e^x - 2x  e^x + 2e^x + C`

`= e^x (x^2 - 2x + 2) + C`

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Chapter 7: Integrals - Exercise 7.6 [Page 327]

APPEARS IN

NCERT Mathematics Class 12
Chapter 7 Integrals
Exercise 7.6 | Q 3 | Page 327

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