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  • Explain Solution R.D. Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 36 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions  Question 36 Maths Textbook Solution.

Answers (1)

Answer:

e^{x} \cos x+C

Given:

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

Hint:

You must know the rule to integrate by parts.

Explanation:

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

\begin{aligned} &=\int e^{x} \cos x d x-\int e^{x} \sin x d x \\ &=\cos x e^{x}+\int e^{x} \sin x d x-\int e^{x} \sin x d x \ldots . .\left\{\int u \cdot v d x=u \int v d x-\int \frac{d u}{d x} \int v d x d x\right\} \\ &=\cos x e^{x}+C \end{aligned}

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