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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 5

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


\begin{aligned} &\int e^{x}(\sin x+\cos x) d x \\ &\int e^{x} \sin x d x+\int e^{x} \cos x d x \\ &=e^{x}(\sin x)-\int \cos x \cdot e^{x} d x+\int e^{x} \cos x d x \end{aligned}
=e^{x}(\sin x)+c                                                                     \left [ \int uv dx=u\int v dx-\left \{ \int \frac{d}{dx}u . \int v dx \right \} dx \right ]


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