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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short answers Question 22

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short answers Question 22

Answers (1)

Answer:

\frac{1}{4}e^{2x^{2}}+c

Hint: You must know about the integral rule of logarithm and exponential functions.

Given: \int e^{2x^{2}+\ln x}dx

Solution: I=\int e^{2x^{2}+\ln x}dx

        =\int x.e^{2x^{2}}dx                                                      \left [ e^{\log x} =x\right ]                              

Let x^{2}=t  and differentiate both sides, \frac{d}{dx}x^{n}=nx^{n-1}

2xdx=dt

I=\frac{1}{2}\int e^{2t}dt

=\frac{e^{2t}}{4}+c                                                                 \left [ \int e^{ax} dx=\frac{e^{ax}}{a}\right ]

=\frac{1}{4}e^{2x^{2}}+c

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