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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 20 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 20 Maths Textbook Solution.

Answers (1)

Answer: -\cos x \log (\cos x)+\cos x+c

Hint: Consider the first function as log(cos x) and second function as sin x

Given: Let I=\int \sin x \log (\cos x) d x

Solution: I=\int \sin x \log (\cos x) d x

                  \begin{aligned} &=\log (\cos x) \int \sin x d x-\int\left(\frac{d}{d x} \log (\cos x) \int \sin x d x\right) d x \\ &=-\cos x \log (\cos x)+\int \frac{-\sin x}{\cos x} \cos x d x \end{aligned}

So we get,

             =-\cos x \log (\cos x)-\int \sin x d x

Again by integrating the second term

           =-\cos x \log (\cos x)+\cos x+c

 

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