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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 38

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 38

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Answer: \frac{1}{3}\log \left | 1+x^{3} \right |+c

Given: \int \frac{x^{2}}{1+x^{3}}dx

Solution: \int \frac{x^{2}}{1+x^{3}}dx
Put 1+x^{3} = t   and differentiate both sides,  \left [ \frac{d}{dx} x^{n}=nx^{n-1}\right ]

3x^{2}dx=dt

x^{2}dx=\frac{dt}{3}

\begin{aligned} &\int \frac{d t}{3 t}=\frac{1}{3} \int \frac{d t}{t} \\ &=\frac{1}{3} \log |t|+c \\ &=\frac{1}{3} \log \left|1+x^{3}\right|+c \quad\quad\quad\quad\quad\quad\quad\left[\int \frac{1}{x} d x=\log x+c\right] \end{aligned}

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