The correct option is B e^xsinx+c we know that ∫ e^x [ f(x)+f^'(x) ]dx= e^x f(x)+c so, ∫ e^x(sinx+cosx)dx= e^xsinx+c ...

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Definition of Limit

∫ exsinx+cos ...

Question

$\int e^{x} (s i n x + cos x) d x =$

e^{x} s i n x + c

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e^{x} c o s x + c

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e^{x} (s i n x - c o s x) + c

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- e^{x} c o s x + c

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Solution

The correct option is B $e^{x} s i n x + c$
$w e k n o w t h a t \int e^{x} [f (x) + f^{^{'}} (x)] d x = e^{x} f (x) + c$
$s o, \int e^{x} (s i n x + c o s x) d x = e^{x} s i n x + c$

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\int e^{x} (sin x + cos x) d x

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\int e^{x} (cos x - sin x) d x =

e^{x} log sec x + c

\int e^{x} (tan x + {sec}^{2} x) d x =

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$\int e^{x}$ (sin x + cos x)dx is equal to -

\frac{e^{x} sin x - cos x}{e^{x} cos x + sin x} = 0

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