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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 46 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise 18.25 Question 46 Maths Textbook Solution.

Answers (1)

Answer: x\: \sin \: x+\cos x-\frac{1}{4}\cos 2x+c

Given: \int \left ( e^{logx}+\sin \: x \right )\cos \: xdx

Hint: Put e^{logx}=x

Solution:\int \left ( e^{logx}+\sin \: x \right )\cos \: xdx

As e^{logx}=x

               \begin{aligned} &I=\int(x+\sin x) \cos x d x \\ &=\int x \cos x d x+\int \sin x \cos x d x \\ &=x \sin x-\int 1 \sin x d x+\frac{1}{2} \int \sin (2 x) d x \\ &=x \sin x-(-\cos x)+\frac{1}{2} \frac{1}{2}(-\cos 2 x)+c \\ &=x \sin x+\cos x-\frac{1}{4} \cos 2 x+c \end{aligned}

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