e-x-sinx-dx-plz-give-me-answer-soon-

Question Number 1000 by rpatle69@gmail.com last updated on 13/May/15

\int e^{x} s i n x d x = ? p l z g i v e m e a n s w e r s o o n .

Commented by rpatle69@gmail.com last updated on 13/May/15

p l e a s e s o o n g u y s

Answered by prakash jain last updated on 13/May/15

I = \int e^{x} \sin x d x

I ntegrate by parts

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

I ntegrate e^{x} \cos x b y p a r t s

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

= - e^{x} \cos x + e^{x} \sin x - I

2 I = e^{x} \sin x - e^{x} \cos x

I = \frac{1}{2} (e^{x} \sin x - e^{x} \cos x) + C

\frac{d}{d x} [\frac{1}{2} (e^{x} \sin x - e^{x} \cos x) + C]

= \frac{1}{2} [e^{x} \sin x + e^{x} \cos x - e^{x} \cos x + e^{x} \sin x]

= e^{x} \sin x

Commented by rpatle69@gmail.com last updated on 13/May/15

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