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Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 1 Maths Textbook Solution.

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Answer: x \sin x+\cos x+c

Hint: \int u v d x=u \int v d x-\int \frac{d}{d x} u \int v d x

Given: I=\int x \cos x d x

Solution:Using integration by parts

I=x \int \cos x d x-\int \frac{d}{d x} x \int \cos x d x

We have,\int \sin x d x=-\cos x, \int \cos x d x=\sin x

\begin{aligned} &=x \times \sin x-\int \sin x d x \\ &=x \sin x+\cos x+c \end{aligned}

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