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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 4

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Answer:e^{x}\left(\sin x \right )+c

Hint: You must know about the integration rule of sin, cos and exponential function

Given: \int e^{x}\left(\sin x+\cos x \right )dx


\int e^{x}\left(\sin x+\cos x \right )dx

\int e^{x}\sin x dx+\int e^{x}\cos x dx

= e^{x}\left(\sin x\right) -\int \cos x.e^{x}dx+\int e^x \cos x dx

  = e^{x}\left(\sin x \right )+c                                    


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