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Explain Solution R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 26 Maths Textbook Solution.

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Answer: 2[\sqrt{x} \sin \sqrt{x}+\cos \sqrt{x}]

Hint: \sqrt{x}=t

Given: \int \cos \sqrt{xdx}

Solution: Put \sqrt{x}=t \Rightarrow \frac{1}{2 \sqrt{x}} d x=d t

\therefore \int \cos \sqrt{x} d x=2 \int t \cos t d t

                  [Using integration by parts]

                    \begin{aligned} &I=2\left[t \sin t-\int 1 \sin t d t\right] \\ &=2[t \sin t+\cos t] \\ &=2[\sqrt{x} \sin \sqrt{x}+\cos \sqrt{x}]+c \end{aligned}


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