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Question

ex(1 x1 + x2)2dx


A

+ C

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B

+ C

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C

+ C

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D

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Solution

The correct option is B

+ C


Whenever there is ex in the integrand the first thing we have to see is that whether it is ex [f(x) + f'(x)]dx form or not. If yes, we'll use the corresponding formula, and if not we'll consider other methods. Let's try to simplify the above given integral and see whether it is of

ex [f(x) + f'(x)]dx form

ex (1 x1 + x2)2dx

ex1 + x2 2x(1 + x2)2dx

ex1 + x2(1 + x2)2 2x(1 + x2)2dx

ex1(1 + x2) 2x(1 + x2)2dx

2x(1 + x2)2 could be the derivative of 1(1 + x2). Let's check.

ddx1(1 + x2) = (1 + x2)(0) 2x(1)(1 + x2)2 = 2x(1 + x2)2

So, ex1(1 + x2) 2x(1 + x2)2dx is the form of ex [f(x) + f'(x)]dx and hence the answer for this integral would be equal to ex11 + x2 + C


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