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

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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}


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

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


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