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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 7

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 7

Answers (1)

Answer:

\frac{1}{2} e^{2 \sin x}+c

Hint:

Simplify the function and then integrate it.

Solution:

I=\int \cos x e^{2 \sin x} d x

Let  \sin x=y                     …(i)

\begin{aligned} &\Rightarrow \cos x d x=d y \\ &\Rightarrow I=\int e^{2 y} d y \\ &I=\frac{e^{2 y}}{2}+c \end{aligned}

 

I=\frac{e^{2 \sin x}}{2}+c               …from equation (i)

 

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