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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 2

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Answer: \frac{x^{8}}{8}+c

Hints: you must know about the integration values of exponential and logarithm function

Given:\int e^{3\log x}x^{4}dx


\int e^{3\log x}x^{4}dx

= \int e^{\log x^{3}}x^{4}dx                                                           [\therefore a \log x=\log x^{a}]

= \int{ x^{3}}x^{4}dx                                                                 [\therefore e^{\log m} = m]

= \int{ x^{7}}dx                                                                      \left [ \int x^{n} dx= \frac{x^{n+1}}{n+1}+ c \right ]


\int e^{3\log x}x^{4}dx=\frac{x^{8}}{8}+c


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