The value of ∫ex+9cosx−2sinx+7ex+7sinx+11cosx+14dx is (where c is the constant of integration)
A
12(x+ln(ex+7sinx+11cosx+14))+c
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B
12(x−ln(ex+7sinx+11cosx+14))+c
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C
x+12ln(ex+7sinx+11cosx+14))+c
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D
x−12ln(ex+7sinx+11cosx+14))+c
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Solution
The correct option is A12(x+ln(ex+7sinx+11cosx+14))+c ∫ex+9cosx−2sinx+7ex+7sinx+11cosx+14dx ∫12(ex+7sinx+11cosx+14)+12(ex+7cosx−11sinx)(ex+7sinx+11cosx+14)dx =12∫dx+12∫ex+7cosx−11sinx(ex+7sinx+11cosx+14)dx =x2+12ln(ex+7sinx+11cosx+14)+c