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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 16

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 16

Answers (1)

Answer:

x^{x}+c

Hint:

By putting x^{x}= y, Simplify it and integrate it.

Solution:

I=\int x^{x}(1+\log x) d x

Let  x^{x}= y               …(i)

Applying logarithm on both sides

\begin{aligned} &\log x^{x}=\log y \\ &x \log x=\log y \end{aligned}

 

diff. both sides

 

\left(x \cdot \frac{1}{x}+\log x\right) d x=\frac{1}{y} d y

(1+\log x) d x=\frac{d y}{y}            …(ii)

\begin{aligned} &\Rightarrow I=\int y \frac{d y}{y} \\ &I=\int d y \\ &I=y+c \end{aligned}

 

I=x^{x}+c                    …from equi (i)

 

Posted by

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