The correct option is A e^x/2 ( sin x cos x ). ∫ e ^ x sin x dx = e ^ x sin x ∫ e ^ x cos x dx = e ^ x sin x e ^ x cos x ∫ e ^ x sin ...

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Domain

∫ exsin xdx.

Question

$\int e^{x} sin x d x .$

\frac{e^{x}}{2} (sin x - cos x) .

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\frac{e^{x}}{4} (sin x - cos x) .

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\frac{e^{x}}{2} (sin x + cos x) .

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\frac{e^{x}}{2} (cos x - sin x) .

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Solution

The correct option is A $\frac{e^{x}}{2} (sin x - cos x) .$
$\int e^{x} sin x d x = e^{x} sin x - \int e^{x} cos x d x = e^{x} sin x - e^{x} cos x - \int e^{x} sin x d x \Rightarrow 2 \int e^{x} sin x = e^{x} sin x - e^{x} cos x \Rightarrow \int e^{x} sin x = \frac{1}{2} (e^{x} sin x - e^{x} cos x)$

Suggest Corrections

Similar questions

\int e^{x} sin x d x = \frac{e^{x}}{2} (sin x - cos x) + c .

\int e^{x} (f (x) + f^{'} (x)) d x = e^{x} f (x) + c .

If $y = s i n x + e^{x}, t h e n \frac{d^{2} x}{d y^{2}} =$

\int e^{x} cos (x) d x = F (x) + c,

c

F (x) =

(a) e^{x} (sin x - cos x)

(b) e^{x} (sin x + cos x)

(c) \frac{e^{x}}{2} (sin x - cos x)

(d) \frac{e^{x}}{2} (sin x + cos x)

S = e^{x} - sin x

\frac{d^{2} S}{d x^{2}}

\frac{sin x + e^{x}}{cos x + e^{x}}

x

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