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Question

The value of ex+9cosx2 sinx+7ex+7sinx+11cosx+14 dx is
(where c is the constant of integration)

A
12 (x+ln (ex+7sinx+11cosx+14))+c
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B
12 (xln (ex+7sinx+11cosx+14))+c
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C
x+12 ln (ex+7sinx+11cosx+14))+c
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D
x12 ln (ex+7sinx+11cosx+14))+c
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Solution

The correct option is A 12 (x+ln (ex+7sinx+11cosx+14))+c
ex+9cosx2 sinx+7ex+7sinx+11cosx+14dx
12 (ex+7sinx+11cosx+14)+12(ex+7cosx11sinx)(ex+7sinx+11cosx+14)dx
=12 dx+12ex+7cosx11sinx(ex+7sinx+11cosx+14)dx
=x2+12 ln (ex+7sinx+11cosx+14)+c

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