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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 10 Maths Textbook Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 10 Maths Textbook Solution.

Answers (1)

Answer:

-\frac{1}{\log _{e} 2}

Given:

\int \frac{2^{\frac{1}{x}}}{x^{2}} d x=K 2^{\frac{1}{x}}+C

Hint

Using  \int a^{x} d x

Explanation:

Let =\int \frac{2^{\frac{1}{x}}}{x^{2}} d x                                    \text { [Put } \frac{1}{x}=t \Rightarrow-\frac{1}{x^{2}} d x=d t \Rightarrow \frac{d x}{x^{2}}=-d t

      \begin{aligned} &=-\int 2^{t} d t \\ &=-\frac{2^{t}}{l o g_{e} 2}+2 \end{aligned}

      =-\frac{2 \frac{1}{x}}{\log _{e} 2}+2                                \left[\because \int a^{x} d x=\frac{a^{x}}{\log _{e} a}\right]

According to given:I=K 2^{\frac{1}{x}}+C

                 \therefore K 2^{\frac{1}{x}}+C=-\frac{1}{\log _{e} 2} \cdot 2^{\frac{1}{x}}+C

Comparing both sides,

               K=\frac{-1}{\log _{e} 2}

 

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